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Paper Citation Record · LEDGER

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models

As of 12 August 2026, this Paper Citation Record lists 62 of 62 outbound references and 1 inbound Pith citation observation for arXiv:2412.08964.

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

pith.paper-citation-record.v1
2412.08964 v2

Coverage vector

measured 62 of 62 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T17:29:42.339631Z

measured 63 of 63 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T11:14:46.367409Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-11T11:14:46.557929Z

Reference resolution

62 of 62 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9c93b897-441f-48aa-9fc4-6c4b80630895 · outbound

This paper cites Strict Convexity of the Surface Tension for Non-convex Potentials.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Strict Convexity of the Surface Tension for Non-convex Potentials

Reference 1

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation db3a286b-60ef-4f84-a6a2-095434c7c1fb · outbound

This paper cites Cauchy-Born Rule from Microscopic Models with Non-convex Potentials.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Cauchy-Born Rule from Microscopic Models with Non-convex Potentials

Reference 2

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local_arxiv, observed 2026-08-11T17:29:42.671429Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation bac27b54-2c8b-455e-8554-aece6a3c2076 · outbound

This paper cites A ¨ıd´ekon (2013).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models A ¨ıd´ekon (2013)

Reference 3

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 11b3321a-96a9-4302-a39f-0b7dc9d3a195 · outbound

This paper cites Depinning in integer-restricted Gaussian Fields and BKT phases of two-component spin models.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Depinning in integer-restricted Gaussian Fields and BKT phases of two-component spin models

Reference 4

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 5da83aad-8d40-4436-9311-4bac533a319b · outbound

This paper cites The scaling limit of the continuous solid-on-solid model.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models The scaling limit of the continuous solid-on-solid model

Reference 5

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Observation 8b92022d-69f5-4fc9-a526-2163024f022c · outbound

This paper cites Bauerschmidt and T.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Bauerschmidt and T

Reference 6

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 33f30d54-3e4a-48bc-897e-895a2f980329 · outbound

This paper cites Bauerschmidt, J.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Bauerschmidt, J

Reference 7

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Observation 97ef566b-b00c-4817-a049-7afa59207db6 · outbound

This paper cites Bauerschmidt, J.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Bauerschmidt, J

Reference 8

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 8ed20750-5642-4315-a452-8122da573e02 · outbound

This paper cites B ¨aumler.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models B ¨aumler

Reference 9

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 953ab1c7-8c09-437e-8286-f0e688a30d71 · outbound

This paper cites Benfatto, G.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Benfatto, G

Reference 10

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Observation 31de0db4-37fc-4721-9713-f9926818091f · outbound

This paper cites Benfatto and J.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Benfatto and J

Reference 11

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Observation 2505743e-70b8-4879-85dc-c313c37a8601 · outbound

This paper cites Berezinskii (1971).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Berezinskii (1971)

Reference 12

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 531d06dd-37fa-4e64-8ae8-c21fb31aaf73 · outbound

This paper cites Biskup (2011).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Biskup (2011)

Reference 13

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation d54acc17-b7fa-4aa9-9a03-d540b595602d · outbound

This paper cites Biskup (2020).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Biskup (2020)

Reference 14

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 5c23cd1b-73c6-45d9-a1c0-501d37695091 · outbound

This paper cites A limit law for the maximum of subcritical DG-model on a hierarchical lattice.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models A limit law for the maximum of subcritical DG-model on a hierarchical lattice

Reference 15

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Unavailable: canonical work link unavailable.

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Observation d8041258-c74b-48fa-a7fd-0fab88b1150a · outbound

This paper cites Biskup and O.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Biskup and O

Reference 16

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Observation c37f445f-41f6-4efd-a842-b4eb80a72b2b · outbound

This paper cites Biskup and O.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Biskup and O

Reference 17

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation f43f38fa-0b1d-4b93-91da-b3a5c25a4218 · outbound

This paper cites Biskup and O.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Biskup and O

Reference 18

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation b7f48c4d-efa7-4063-9a37-599b0f3b08f1 · outbound

This paper cites Biskup and H.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Biskup and H

Reference 19

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation a92b7c96-3e42-43aa-ad81-d9b583a8c8b8 · outbound

This paper cites Bleher and Ya.G.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Bleher and Ya.G

Reference 20

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verified fuzzy
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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 990c2452-d1ee-4f94-989c-8acad3e56edc · outbound

This paper cites Bleher and Ya.G.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Bleher and Ya.G

Reference 21

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 59b7b92f-9fc3-49cf-8556-49cb579a4f50 · outbound

This paper cites de Almeida Braga (1989).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models de Almeida Braga (1989)

Reference 22

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 295bff7a-df86-48d1-a1f9-b203d27bd90e · outbound

This paper cites Bramson, J.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Bramson, J

Reference 23

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation cba593a1-2b6b-4a65-8b93-512cbfe4183d · outbound

This paper cites Bricmont, J.R.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Bricmont, J.R

Reference 24

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 2aac547b-faff-4b20-b0c6-dbc7ad36ef67 · outbound

This paper cites Brydges (2009).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Brydges (2009)

Reference 25

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 9d56ccbf-f016-439b-94e3-3c31d7a35397 · outbound

This paper cites Brydges and T.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Brydges and T

Reference 26

Resolution
verified fuzzy
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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation fdea8bbd-8fd8-43ec-8232-3440cb7ffbf3 · outbound

This paper cites Quantitative delocalisation for the Gaussian and $q$-SOS long-range chains.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Quantitative delocalisation for the Gaussian and $q$-SOS long-range chains

Reference 27

Resolution
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation d223218c-d73d-4354-bc23-1c76f8c31c4d · outbound

This paper cites Cotar, J.-D.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Cotar, J.-D

Reference 28

Resolution
verified fuzzy
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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 7185faf3-f534-4734-a1ee-eb30c330aedf · outbound

This paper cites Upper bounds on the fluctuations for a class of degenerate convex $\nabla \phi$-interface models.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Upper bounds on the fluctuations for a class of degenerate convex $\nabla \phi$-interface models

Reference 29

Resolution
verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 2d4b2205-5d04-499d-9426-ffbc017827cb · outbound

This paper cites Hydrodynamic limit for a class of degenerate convex $\nabla \varphi$-interface models.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Hydrodynamic limit for a class of degenerate convex $\nabla \varphi$-interface models

Reference 30

Resolution
unresolved
no resolver link, observed 2026-08-11T17:29:42.052621Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T17:29:42.052621Z digest=sha256:8f43540e1aa98988e7a22a2507d534982bf0d790f549e59680eb3819def4b041

Observation e90f1d4c-0e8f-4e65-bdb5-afaef2da1bfc · outbound

This paper cites Dimock and T.R.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Dimock and T.R

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:43.003158Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 35ee0678-5b18-40df-81ce-dedfad93b4d6 · outbound

This paper cites Dobrushin (1972).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Dobrushin (1972)

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.991597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 99fdc66f-db7d-499d-a7f0-c866a729d0ca · outbound

This paper cites Dyson (1969).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Dyson (1969)

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.977207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 4bf939fa-c55c-4a90-ab5f-115adf2709c5 · outbound

This paper cites Falco (2012).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Falco (2012)

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.967059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation b412d4a8-60e4-4e7c-8253-03b554ceba33 · outbound

This paper cites Critical exponents of the two dimensional Coulomb gas at the Berezinskii-Kosterlitz-Thouless transition.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Critical exponents of the two dimensional Coulomb gas at the Berezinskii-Kosterlitz-Thouless transition

Reference 35

Resolution
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 727d631a-7168-4113-ae52-9164d2aa87a1 · outbound

This paper cites Fr ¨ohlich and Y.M.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Fr ¨ohlich and Y.M

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.957044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.075885Z digest=sha256:e2e2c7739e778d9876d9c7806c03ed253582c32ecb56badc522d1ecd9a2989f6

Observation c72bafce-b4ad-497e-b9e4-033314f9e4ca · outbound

This paper cites Fr ¨ohlich and T.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Fr ¨ohlich and T

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.947708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.080371Z digest=sha256:edadfa1b301537f5cc6bd35686a9c4eec3fa89a73cb76a93ff12983253e05135

Observation c5c91951-6631-4c7b-b725-bc36b39278de · outbound

This paper cites Fr ¨ohlich and B.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Fr ¨ohlich and B

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.935758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.084595Z digest=sha256:86f10da0e135a04466658ba3d35c7e4e7425db2e68f9c559c05505e014035772

Observation a871d223-6f5d-4677-880d-13caa6e22720 · outbound

This paper cites an unresolved cited work.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-11T17:29:42.923030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.089043Z digest=sha256:4feaa76dabbce7a0705bc8edd7e945b39d57832353ed1c704e3cc27533cfef4f

Observation 3ddf335b-50d3-4cf1-8f51-120d001ca749 · outbound

This paper cites Invisibility of the integers for the discrete Gaussian chain via a Caffarelli-Silvestre extension of the discrete fractional Laplacian.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Invisibility of the integers for the discrete Gaussian chain via a Caffarelli-Silvestre extension of the discrete fractional Laplacian

Reference 40

Resolution
unresolved
no resolver link, observed 2026-08-11T17:29:42.092890Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T17:29:42.092890Z digest=sha256:3ce62d663968198b6d1c74789b6075d109ee6d9e2b69ef7e8880fc6cc77a8e2a

Observation 89d64896-45ab-4c32-8680-4193e54db7d4 · outbound

This paper cites Garban and A.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Garban and A

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.912229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.097082Z digest=sha256:846fbf2bac776684933d643d90e56af43b8f5d92f3308085f1e1bd8d7c9db18d

Observation bc2b5df3-f002-4fae-b38f-0239f07ddce7 · outbound

This paper cites Gawe ¸dzki and A.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Gawe ¸dzki and A

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.901469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.100519Z digest=sha256:e27285069ef29c4511e947a5469b6bd971f93781188bfda7f23cb377e25f577d

Observation d20f5455-a5fa-4c97-a082-b63420791b26 · outbound

This paper cites Giacomin, S.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Giacomin, S

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.887778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.104495Z digest=sha256:2942cb09c8a8287025d5619aa3de14a292f2fa10709fe51497e2c0179d232ae5

Observation 1c75e17a-741b-437e-b0b4-77c0a7e465b0 · outbound

This paper cites Guidi and D.H.U.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Guidi and D.H.U

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.877847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.109767Z digest=sha256:aad97c6c4e6bffce89ca5f5fb635118d15a19fdb69341bed86a68f847b6112d4

Observation 1a631b6b-551b-45c7-add1-21087e816bca · outbound

This paper cites an unresolved cited work.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-11T17:29:42.867340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.114297Z digest=sha256:426a2f2c5b64ebd25f770bc56596fc36580a409b89a6afd33029dbbc2b481c3d

Observation 968f6667-c4ab-4da3-9b74-55de5fff6e04 · outbound

This paper cites Critical cluster volumes in hierarchical percolation.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Critical cluster volumes in hierarchical percolation

Reference 46

Resolution
verified exact
local_arxiv, observed 2026-08-11T17:29:42.490781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.118943Z digest=sha256:f26ede48e5905ac8ac111b595f70ef46da8fa9406f1b1ad7446ed3ddb2a8a253

Observation a4f64db4-3258-484f-bd18-fc1882b96339 · outbound

This paper cites Hutchcroft (2024).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Hutchcroft (2024)

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.857509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.124431Z digest=sha256:18503a842a8dcc3d219ecf7cea482043cd3ec089d917d21013614824f42552d6

Observation 2a65d908-5934-4767-89ec-90c88d55b3b5 · outbound

This paper cites The Fr\"ohlich-Spencer Proof of the Berezinskii-Kosterlitz-Thouless Transition.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models The Fr\"ohlich-Spencer Proof of the Berezinskii-Kosterlitz-Thouless Transition

Reference 48

Resolution
unresolved
no resolver link, observed 2026-08-11T17:29:42.130057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T17:29:42.130057Z digest=sha256:fb44570dabc54642dbd5f852c962e40a9957a688d1e6227cb16da98512e3b67b

Observation 99096e9b-72d3-40f2-a3fa-49ee55dae1cc · outbound

This paper cites Kjaer and H.J.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Kjaer and H.J

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.845827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.134737Z digest=sha256:ec7a84aeb3e27119bc3988bf6903a0d03f8adf1685df4138be6b62b7a15bab23

Observation 9168d60e-9d77-4fdc-860d-50788764880d · outbound

This paper cites Kosterlitz and D.J.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Kosterlitz and D.J

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.833455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.139102Z digest=sha256:9d88259960d5e816c32809f7557320fbac494a5cdf4dee54a3dd921e0b698c9f

Observation 9873b699-d2af-49ba-a888-3c41863a701e · outbound

This paper cites Lammers (2022).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Lammers (2022)

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.819812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.144359Z digest=sha256:06ca2e29dc94296fc78dfff0b8d3c5b66edd0ddfbf3a68d12931afc79ef408d3

Observation d4a4863a-a00b-4436-9511-7e4897b8d8ba · outbound

This paper cites Lubetzky, F.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Lubetzky, F

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.808416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.148802Z digest=sha256:88490d12985a11a36e444d1b98e32ca26db1e6ae6ea089728c77c1746d02388c

Observation bad8416b-f79e-46d5-9352-f43adb9d38b2 · outbound

This paper cites Madaule (2017).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Madaule (2017)

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.796526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.152914Z digest=sha256:530c0c712fe1725bfdb5033c9f4ad4df107ac35e25288770480ed1e5864aa98c

Observation a93a4afd-188a-44aa-a523-662e37698859 · outbound

This paper cites Marchetti (1992).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Marchetti (1992)

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.785414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.157882Z digest=sha256:e83d284d4e5988f0148911df5a54977607b881fddfd135f0b11ffea6771dc4ce

Observation ab205384-e67b-47ff-98c8-bd82ccbb5375 · outbound

This paper cites Marchetti and A.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Marchetti and A

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.773089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.162985Z digest=sha256:82c6006bec61b261af7d2adf2a172218e23f395d3b235e16b115ed79ebfd79ff

Observation d29a094e-beee-498f-82e8-afdd8a9f0b34 · outbound

This paper cites Marchetti and J.F.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Marchetti and J.F

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.762637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.173771Z digest=sha256:a36b759ade85bc4189115d2b6d0171de45bbe121960b513e867816ca6f45cd35

Observation 14c9629e-7ba2-4372-894f-ee80ac1fb533 · outbound

This paper cites Naddaf and T.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Naddaf and T

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.749354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.214211Z digest=sha256:446c990373182a467ea5e9a009e12809643f7ab2306402651ec0f5c9589e0b2f

Observation 115a3566-1376-4f6a-a9f7-2de4f4c76b63 · outbound

This paper cites Central Limit Theorem for Multi-Point Functions of the 2D Discrete Gaussian Model at high temperature.

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Central Limit Theorem for Multi-Point Functions of the 2D Discrete Gaussian Model at high temperature

Reference 58

Resolution
unresolved
no resolver link, observed 2026-08-11T17:29:42.254046Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T17:29:42.254046Z digest=sha256:d522a31571ce174314b2ae562dbaac627909f0282e2c8e023f914e70d4a89a37

Observation 87d0cf14-89db-4874-b78d-0321f9b9b55c · outbound

This paper cites Sheffield (2005).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Sheffield (2005)

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.735908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.303431Z digest=sha256:e519a15fa493284a22b7c6dd0e4a1559e5ce6b0d04311269bbe411b4d6f8300a

Observation d11aacca-15ab-4d74-b53d-e1aecddae59f · outbound

This paper cites Siegert (1960).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Siegert (1960)

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.725143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.330491Z digest=sha256:51706046d3e51a490de890a8177246a4ff484d0d35ae0e43540724a08d8a8dff

Observation 26f0a12e-20c5-4dfa-97da-c79ac2e38714 · outbound

This paper cites Velenik (2006).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Velenik (2006)

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.713959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.335375Z digest=sha256:e76a48c6e765fd1be03feff58b400c4cdc4131061c5b2399c864a90ea323ee62

Observation d1f832f2-1b20-4c4b-a70e-de8d04c37490 · outbound

This paper cites Ye (2019).

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models Ye (2019)

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T17:29:42.701440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T17:29:42.339631Z digest=sha256:dfd96489c991dcc6a7a4aafc7ae8fda63d0c0e3197339463c77f633650225160

Pith citing papers

Observation c253ab8f-d257-4042-a75b-32bfd6048439 · inbound

Quantitative delocalisation for the Gaussian and $q$-SOS long-range chains cites this paper.

Quantitative delocalisation for the Gaussian and $q$-SOS long-range chains Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models

Reference 6

Resolution
verified exact
local_arxiv, observed 2026-08-11T11:14:46.560656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T11:14:46.367409Z digest=sha256:d7b8ed9359f5259ccc14da91ffefd37aa91f9fc9fa7cb19157a71b91d7984629