Pith. sign in

Paper Citation Record · LEDGER

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models

As of 17 August 2026, this Paper Citation Record lists 83 of 83 outbound references and 2 inbound Pith citation observations for arXiv:1908.07502.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.07502 v2

Coverage vector

measured 83 of 83 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T12:34:15.778461Z

measured 85 of 85 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T10:12:04.988167Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-04T14:49:56.049728Z

Reference resolution

83 of 83 outbound references displayed

  • verified exact5
  • verified fuzzy51
  • unresolved27
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.372759Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.372759Z digest=sha256:ce7d1d80800a2a6c2daccd70a3e803a5fa3a4c69c12137efe09d1745638db1b3

Reference 2

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unresolved
no resolver link, observed 2026-08-14T12:34:15.379244Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.379244Z digest=sha256:386938550a87d8acd6d908c0efad95d6ac66229751337ea5f652f5da7f923ede

Reference 3

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unresolved
no resolver link, observed 2026-08-14T12:34:15.384247Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.384247Z digest=sha256:98e8d8742012ca01c083d3cab7bb15489b2026e8a4d39b14117b91a05e483c96

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:17.065727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.389041Z digest=sha256:66e079a9ea47be9b57ece4a17fdce0e030239daee36fc66673a4cf5fbb9b51c2

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:17.051571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.394033Z digest=sha256:dfcbd21014a49bd937204517fa68bf26e88c8a3744c2ec1bf5ab06c67ec14cfa

Reference 6

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verified fuzzy
raw_fallback, observed 2026-08-14T12:34:17.037026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.398975Z digest=sha256:6f262036374a1880e12b8f70705674cef9dffafc3a34867b5b38d3d018f210e7

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:17.022095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.403677Z digest=sha256:d206fa38af1ba4ffe6fdb7024b361a9474bbdc13614599d53c326d25e749fd10

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:17.006938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.408581Z digest=sha256:f2fa2a58f57568c7e7baca0a2d95cd9d64b4101349fce3a18094bd234ea5da20

Observation baf9bb58-9dcb-471c-b05e-67f8bc8ced72 · outbound

This paper cites Six loop analytical calculation of the field anomalous dimension and the critical exponent $\eta$ in $O(n)$-symmetric $\varphi^4$ model.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Six loop analytical calculation of the field anomalous dimension and the critical exponent $\eta$ in $O(n)$-symmetric $\varphi^4$ model

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.412880Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.412880Z digest=sha256:a51bd422d2ecbfdd4e567ce965e211dbcad6362ad46316bf217c354b6c07d873

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.417624Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.417624Z digest=sha256:cd74abdba8f590fdb4e25e3e9dfa524408335f9096ee025b128088a741be7c46

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.422900Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.422900Z digest=sha256:4c026e9c2ed00fc9787aabccd5a4985a053bc38c24434f1bb7ae46dd754a68e4

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.991998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.427629Z digest=sha256:fe15cf84d82685959c59395f8bf898234cf23a4235abdd4fed0cc8484029dfa8

Observation 93f6a74b-ea49-44f1-afd1-e3f0b181aff4 · outbound

This paper cites Zinn-Justin, Quantum Field Theory and Critical Phenomena, Oxford University Press, Oxford, 1989.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Zinn-Justin, Quantum Field Theory and Critical Phenomena, Oxford University Press, Oxford, 1989

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.976150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.431980Z digest=sha256:0bf69ac8a95887fee304d92115bbb828682c98c5e341b18282b2ba1803192d59

Observation 18df1ee0-bdaa-4fe1-9203-8b102af016ff · outbound

This paper cites Vasil’ev, The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics , Chapman & Hall/CRC, New York, 2004.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Vasil’ev, The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics , Chapman & Hall/CRC, New York, 2004

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.959496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.436115Z digest=sha256:891914988db9e312acccb97b48c4043dd48ccbd8e4ef13bb2611b3e67bc40e46

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.941339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.440223Z digest=sha256:caa51a5308131aa5ff83ac8fe13bc9ab59f344e6ad88689cc12f98d4b3e9e731

Observation b09d65ce-17db-4d98-aa4a-e57b090981ab · outbound

This paper cites an unresolved cited work.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:34:16.924213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.444797Z digest=sha256:b39734d36be4682ae3d07a6e32198edbb09722f7e8d974dbf2744a935f9ea73f

Observation f4fb92d0-5024-4c5f-98d6-b349ca616240 · outbound

This paper cites an unresolved cited work.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:34:16.909603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.449439Z digest=sha256:5795c6f5663d81ebe21b3b7a4a8c078836106014f21fe412041274a52a28fdfc

Observation feafb657-b7d8-4e68-9cf3-47cb447d0334 · outbound

This paper cites an unresolved cited work.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:34:16.896416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.454305Z digest=sha256:63a12c042dd9b479951340ca05e4b3e0e2be02e1321e248c86df1633efd3617e

Observation 931db104-aca5-4539-977f-238303e86400 · outbound

This paper cites Five-loop renormalization group functions of ${O}(n)$-symmetric $\phi^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Five-loop renormalization group functions of ${O}(n)$-symmetric $\phi^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$

Reference 19

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.459519Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.459519Z digest=sha256:5f142ef5fd773749e804e80468acee2074d693f33daac9bcf751583b3e41cbcb

Observation 3eff728a-8b1c-4f01-b31f-4b22441fd3dc · outbound

This paper cites Schnetz, Numbers and functions in quantum field theory , Phys.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Schnetz, Numbers and functions in quantum field theory , Phys

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.882879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.464351Z digest=sha256:d918470c1eea3b46b51ac0d5516e67af43f94a049d19f9ea093546726046b9fd

Observation 8ad8773b-a68f-42e6-a899-9243c006a125 · outbound

This paper cites Parisi, Statistical Field Theory , Frontiers in Physics, Addison-Wesley, 1988.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Parisi, Statistical Field Theory , Frontiers in Physics, Addison-Wesley, 1988

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.868918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.468834Z digest=sha256:0140d59cc25733cad3e335ed4e82eda359ce6a6f1806258a20fb0d240bdb849d

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.854884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.473397Z digest=sha256:d58efd21bcd6bc8b3049f51eb8c824b00b30891c96e59fa21b69d49932dfbed3

Reference 23

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.477827Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.477827Z digest=sha256:7ea0ca323eb327e5a45cc6900693d5e9d52c707c9cc324199c057dfb50400fe4

Reference 24

Resolution
verified exact
local_arxiv, observed 2026-08-14T12:34:16.129563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.482761Z digest=sha256:90d6dd9abd445fe9cfc7106f36f48de9a08c291cc8068fa05156013e62e33d7d

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.839550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.488000Z digest=sha256:82bf9c2648b7331e29ed443f5685bd2ba370d8491d00e56cf2b45869c6555cad

Reference 26

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.492429Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.492429Z digest=sha256:d2010ff6cc5ee9ffec4960bd9481e588de9289f737c8f2484edf00525bfb19c2

Reference 27

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.497961Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.497961Z digest=sha256:fec825a60ad2a8acf48cb4122f22ab7c7c76a633e3914f197bf504e6e54b960a

Observation b3c0d0cd-5d1d-4cb4-be1f-4cff2aff92ca · outbound

This paper cites Deng, Bulk and surface phase transitions in the three- dimensionalO(4) spin model, Phys.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Deng, Bulk and surface phase transitions in the three- dimensionalO(4) spin model, Phys

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.823979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.503836Z digest=sha256:a0a8da7ab06176772a7027dd7d710e33fc62eee22ccbc807ba34f1f9ecb6ccdb

Observation 9b32e54b-1086-45c2-95c5-2dc3732189d8 · outbound

This paper cites Nienhuis, Coulomb Gas Formulation of Two-dimensional Phase Transitions, V olume11 of Phase Transitions and Critical Phenomena, Academic Press, London, 1987.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Nienhuis, Coulomb Gas Formulation of Two-dimensional Phase Transitions, V olume11 of Phase Transitions and Critical Phenomena, Academic Press, London, 1987

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.809335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.509022Z digest=sha256:35d2a4e29391a1a73c06ac88efb8aa8ca754a47861b473d69cc7bb08be6945ad

Observation 8bbd798c-b8c3-4d80-afdb-218ce69bc179 · outbound

This paper cites Henkel, Conformal Invariance and Critical Phenomena , Springer, Berlin, Heidelberg, 1999.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Henkel, Conformal Invariance and Critical Phenomena , Springer, Berlin, Heidelberg, 1999

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.794940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.513612Z digest=sha256:a20103757d4797e0b9b280d6189d555f2f76a20d96f097ef43d6b446f57f34c2

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.780622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.518992Z digest=sha256:973d36e6894462663ec661d6060ec0e09c50dfc4c0672a611fb50bd222b8eac9

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.767160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.524039Z digest=sha256:3c28249144a6ac593143d2dd31ddcebe99c5a46111a25b44d1bc56465d80ce98

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.753002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.529309Z digest=sha256:4f8dca27837f0e475b4c2ff235241af2f1a84315cf38b5b3c1087e583da01245

Reference 34

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.534577Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.534577Z digest=sha256:b458f7014f18d38ebbf759a94e99a330977dc84b1f1891a98b48b4a274a8cbc3

Reference 35

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.540464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.540464Z digest=sha256:cf2829f66aefea116fb12d8fa983491ade3fce93cad01e74162ebb9d87a6c11a

Reference 36

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.550490Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.550490Z digest=sha256:f1c566cc601d385accf2973d8b25febc06649228ac04d316c1e9594210d408bf

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.738426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.556013Z digest=sha256:70c417fbc9457637fc74a1997b45e7da36a4d6d287b2c64657dfb1b5885a552d

Observation efcc21f9-695a-4e48-b4e2-094a5133b0cd · outbound

This paper cites Zinn-Justin, Precise determination of critical exponents and equation of state by field theory methods, Phys.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Zinn-Justin, Precise determination of critical exponents and equation of state by field theory methods, Phys

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.724002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.560469Z digest=sha256:f231fbf1cc5557ad06afaf9ae0dcbd0da83dc3a5e8433c767cf38911eb673d66

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.710369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.566109Z digest=sha256:1825ba52d71e65c1fa84359c886b776c6d8ce8daec69f670d8dc317ee3e0125f

Observation c26fa7c1-8b06-41e3-8d58-39c9554516d3 · outbound

This paper cites Lawler, A self-avoiding random walk , Duke Math.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Lawler, A self-avoiding random walk , Duke Math

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.695964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.570434Z digest=sha256:69951b5660a6e0d06b144a1b44f5194156c4af97dc1ad388dc3caa7a42065b3d

Observation 4280bf91-b556-4af7-bf76-01439ecf57ea · outbound

This paper cites Falconer, The Geometry of Fractal Sets, Cambridge Uni- versity Press, Cambridge, U.K., 1986.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Falconer, The Geometry of Fractal Sets, Cambridge Uni- versity Press, Cambridge, U.K., 1986

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.681165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.574739Z digest=sha256:603f70fa6af2ce8144ccf3a885933ceb9c90a9a2f9ce942c2d63c2230efc2dbb

Reference 42

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.579196Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.579196Z digest=sha256:0e0ee1f393c1a220464e279f8be68c136dfcdd1ff335e5756b095eec4dea1b49

Observation 7d2eb515-a153-4e74-b568-65fcb55d8c14 · outbound

This paper cites De Gennes, Exponents for the excluded volume problem as derived by the Wilson method, Phys.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models De Gennes, Exponents for the excluded volume problem as derived by the Wilson method, Phys

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.664988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.584496Z digest=sha256:a6080b93f1149fabf7f175f04c3636e7a321a8b83a522f232dcb706584f60a36

Reference 44

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.589131Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.589131Z digest=sha256:2886ca5a63e0d83c41f23ec3f800a9b845d4810d948cac1c95059fcc1335b9e1

Observation 2d50fd31-2729-48f4-84a3-6a1582d3703c · outbound

This paper cites Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric $\phi^4$ theory with $n\to -2$ and loop-erased random walks.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric $\phi^4$ theory with $n\to -2$ and loop-erased random walks

Reference 45

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.594289Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.594289Z digest=sha256:c18c010457341fff5240bb7a406991f2a603a724ff0858963163a21a75269516

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.598950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.598950Z digest=sha256:99ae71704cef6398003fc24fcd27345eb37b700ce51f356a38d5853250aca94b

Reference 47

Resolution
verified exact
local_arxiv, observed 2026-08-14T12:34:15.958741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.603729Z digest=sha256:88ba9f6edb6a9600438af63b353e7c07c2c75d2da80fb5e7ee3f7d65afbb0475

Observation 8921a188-caa5-4a93-9ad3-99869fe1e085 · outbound

This paper cites Hausdorff di- mension of critical fluctuations in Abelian gauge theories.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Hausdorff di- mension of critical fluctuations in Abelian gauge theories

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.648986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.609049Z digest=sha256:205fcc388b941d5edc9025be21bc4e30a3b82a71fa1ec0eddf3a3371833fdf91

Observation 80f77ca3-7fbc-400c-90a9-3e152c4980ed · outbound

This paper cites Kirkham, Calculation of crossover exponent from Heisen- berg to Ising behaviour using the fourth-order ϵ expansion, J.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Kirkham, Calculation of crossover exponent from Heisen- berg to Ising behaviour using the fourth-order ϵ expansion, J

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.633743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.613535Z digest=sha256:f44126096a9f24c64e134c4ac0f4233ab8a7e3c66f0e4b255b70320dbcec11be

Observation dff9123b-9f82-4f32-a3ab-ee67aa4cf8fd · outbound

This paper cites an unresolved cited work.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:34:16.619894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.619100Z digest=sha256:baf11d7700a0907689c425ecf186631cde74a2abc4d4b0ec821cb2cb6ed0093d

Reference 51

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.624219Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.624219Z digest=sha256:6720291520a99dc24efc909df0a77d6e88e348fff6d9bc6f767a7a6e4adca509

Observation fa38ad12-eaaa-40df-ab8b-8222e42b1964 · outbound

This paper cites Kleinert, Variational resummation forϵ-expansions of crit- ical exponents of nonlinear O(n)-symmetricσ-model in 2 +ϵ dimensions, Phys.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Kleinert, Variational resummation forϵ-expansions of crit- ical exponents of nonlinear O(n)-symmetricσ-model in 2 +ϵ dimensions, Phys

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.604514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.629292Z digest=sha256:760924f9cab2f595ccb8545c95363d1f3050b1758a389150d97de1dccfdfea29

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.589690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.633705Z digest=sha256:1a8530495943cdb7bfd41ccf2ab4b65715d236dcc9eb702b906053cda85dd38c

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.573690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.639102Z digest=sha256:92a26ed046c250d093fe71f76fb8464fd28490f47d012e8dae0bbebea4ae5833

Observation 677f0792-a706-4806-8a7e-9a2aabe988a6 · outbound

This paper cites Domann, Optical measurements on TbPO4 near the bicrit- ical point, J.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Domann, Optical measurements on TbPO4 near the bicrit- ical point, J

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.558315Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.643461Z digest=sha256:c730996271e0ebb558af2476f3be785193abf71bc58034e0dc8e9d9e64aabb8c

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.541613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.649485Z digest=sha256:a1f876646076544b97e982efc28d65c92c0dd8a021db8bc3ea30f1e6c98cc0a4

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.526306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.656022Z digest=sha256:8ef48fd59ad3e0082198f1fc72644ffd63be042bf8bab2c335b7569c1aa41bf7

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.511322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.660726Z digest=sha256:cfff9b9103b689ff38a5ce66429a9db091bcdb9cff3f61de6ce28fdcbd9f92b6

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.496742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.665544Z digest=sha256:3d7f02086b278adf9b874bbd7a0b1be415f1652a31875bce98cdae6be49837a7

Observation 343820bd-81c7-49c3-a63e-11be513683e9 · outbound

This paper cites an unresolved cited work.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Unresolved cited work

Reference 60

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:34:16.482071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.670190Z digest=sha256:35cde20270fffcbadb5eb3bf61b2a6cf0a187bd0ec7c9efa08050412a3178240

Observation 46df2136-735a-4b5a-b24a-2dc79fd2a1dc · outbound

This paper cites Zhang, A unified theory based on SO(5) symmetry of su- perconductivity and antiferromagnetism , Science 275 (1997) 1089–1096.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Zhang, A unified theory based on SO(5) symmetry of su- perconductivity and antiferromagnetism , Science 275 (1997) 1089–1096

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.467517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.674952Z digest=sha256:072999df2dba3deb5dfe60645e991407d135fa09fee294b85f0ed2e0390985be

Observation 55a75d00-a8cf-4aab-ba56-ac5daf0b4437 · outbound

This paper cites Hu, Bicritical and tetracritical phenomena and scaling properties of the SO(5) theory , Phys.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Hu, Bicritical and tetracritical phenomena and scaling properties of the SO(5) theory , Phys

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.453185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.679690Z digest=sha256:6bf48eeda70a9ffc2c47cc693b37c500b7d5dfd1bf79fbeb00b12ba782004aed

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.438963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.684145Z digest=sha256:1012df909adb4433c7aafad53ddbb26f265f6baa3be10872b757dde463aa1ffb

Observation 66fbb0aa-69a8-4e30-a8ff-0bfd96af5746 · outbound

This paper cites Bicritical and tetracritical phenom- ena and scaling properties of the SO(5) theory.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Bicritical and tetracritical phenom- ena and scaling properties of the SO(5) theory

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.425250Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.688880Z digest=sha256:8bb1e545b6308461a87508e93c38c8fc0006c9b0407336597b906f756e8f6390

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.411399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.693506Z digest=sha256:4492731b8097a6e872d6eee656317210625ce5f1ea721c69c2d513125e3488a7

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.396262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.698608Z digest=sha256:4f5b1ee3d012bb68317a91f27ed2fc7ecd5f202f351dc901f55bd669366e5e1a

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.382458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.703539Z digest=sha256:bf93568df30b09a4c4ca0ab58d0df8af9cced5d0eb72a8cb5fd66bd4f783f7e4

Reference 68

Resolution
verified exact
local_arxiv, observed 2026-08-14T12:34:15.920160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.707958Z digest=sha256:10c397330a1d20d4aa2b681cf5bd3ba33db410fe5cdb5eff22ead18079dd4e01

Observation 8e51109d-0722-47da-85e7-c6dc9d2d381d · outbound

This paper cites Nienhuis, Exact critical point and critical exponents ofO(n) models in two dimensions , Phys.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Nienhuis, Exact critical point and critical exponents ofO(n) models in two dimensions , Phys

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.368124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.712735Z digest=sha256:18e065c03faaecd7a552105dde119613537d68c42a514ab4ddce81a29a1a91a8

Observation 80c1f464-0a3f-49bc-9dee-a209fec9a285 · outbound

This paper cites Duplantier, Loop-erased self-avoiding walks in two dimen- sions: exact critical exponents and winding numbers , Physica A 191 (1992) 516–522.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Duplantier, Loop-erased self-avoiding walks in two dimen- sions: exact critical exponents and winding numbers , Physica A 191 (1992) 516–522

Reference 70

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.353350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.717033Z digest=sha256:f88f06b6eff2548513a4fb3f89bdee9065b4fc6a46a8726d5463c0c9082a9c36

Reference 71

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.337681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.721540Z digest=sha256:eda0510b140ad9fc8794f144673ebacdc5412e4fca1d2ac53565ac37501b1d49

Observation 3928f556-235f-43de-b1cb-1d4924dd97f9 · outbound

This paper cites Lawler, The Laplacian-b random walk and the Schramm- Loewner evolution, Illinois J.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Lawler, The Laplacian-b random walk and the Schramm- Loewner evolution, Illinois J

Reference 72

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.322169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.726136Z digest=sha256:77a8c0dc396ec92f188d5afafb09891506adc4f48ec0a38f63ff7e2d14c1539f

Reference 73

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.730569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.730569Z digest=sha256:5cfd0d09ca684aed647dd1dc6ea3316184410a2d2b1bda30add2f08ea9aa8f1b

Reference 74

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.305409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.735972Z digest=sha256:75e615e154b652d5694fe475d0548c4ccd293b114d154fe546c0e811975fc7a2

Observation 201ee129-91d3-47cf-95af-68e1b807c181 · outbound

This paper cites an unresolved cited work.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Unresolved cited work

Reference 75

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:34:16.288815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.740729Z digest=sha256:1441910f31a6539096850470fbcf830b234183f86a2c2606e53b781963f1f9a3

Reference 76

Resolution
verified exact
local_arxiv, observed 2026-08-14T12:34:15.883380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.745798Z digest=sha256:572e10bebfdd32f4103705dc0094192022a154665fc4e6584cc1f5ed61bd7e3c

Reference 77

Resolution
verified exact
local_arxiv, observed 2026-08-14T12:34:15.862187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.750819Z digest=sha256:370497247958088334f5ab4d23be1a0cc6bc841bcd54ec3d32add062081edced

Reference 78

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.273714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.756155Z digest=sha256:0e618aafca7d47ce668411641debfe111a11267e420665e4ec2440e1e5d5f40d

Reference 79

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.258517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.760367Z digest=sha256:b054c564736db700025571ec411680a2f90ba49e7930b7ffbcb3ceac64867583

Reference 80

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.242801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.764652Z digest=sha256:33ec25e52de26a9e6a16fcc2a1ee123331b091864958473e69c107b505c8a869

Reference 81

Resolution
unresolved
no resolver link, observed 2026-08-14T12:34:15.769013Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T12:34:15.769013Z digest=sha256:3f6fa34f4f0ae013e8210c4126371507e20f617c302fbe6ea5aa85d6bab5a710

Observation b82c61b5-5bc4-4aaa-abf9-f8914a104df7 · outbound

This paper cites Belohorec, Renormalization group calculation of the uni- versal critical exponents of a polymer molecule , PhD thesis, University of Guelph, Ontario, Canada, 1997.

Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models Belohorec, Renormalization group calculation of the uni- versal critical exponents of a polymer molecule , PhD thesis, University of Guelph, Ontario, Canada, 1997

Reference 82

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:34:16.227199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T12:34:15.773886Z digest=sha256:00e8806838e4691f8b81e138d24be48526e24744ec9696551c67869fb8185121

Reference 83

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no resolver link, observed 2026-08-14T12:34:15.778461Z

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source=pdf_text observed=2026-08-14T12:34:15.778461Z digest=sha256:209326f1bc19beb377f669220ab94e474f20b6f0ec93d6ab390d3a879d62e8ed

Pith citing papers

Observation 8b9a3313-5c48-46a7-88a2-5b1e650fea0c · inbound

Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric $\phi^4$ theory with $n\to -2$ and loop-erased random walks cites this paper.

Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric $\phi^4$ theory with $n\to -2$ and loop-erased random walks Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models

Reference 63

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no resolver link, observed 2026-08-14T10:12:04.988167Z

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source=pdf_text observed=2026-08-14T10:12:04.988167Z digest=sha256:75bc2e1431b218f159fbf5c04a85aceac7b9dcafc30ba9bc0a86cc39115e1e8d

Reference 10

Resolution
verified exact
arxiv_id, observed 2026-07-04T14:49:56.051449Z

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source=pdf_text observed=2026-06-26T02:16:41.442380Z digest=sha256:939987d0b5210800cbdf20a3577ad4fdd9b2b6b62e586bce47ebe8c674b655fb