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arxiv: 2605.06773 · v1 · submitted 2026-05-07 · ❄️ cond-mat.stat-mech · cond-mat.mtrl-sci· cond-mat.soft· cond-mat.str-el· hep-th

Recognition: 2 theorem links

· Lean Theorem

Direct Experimental Test of Conformal Invariance via Grazing Scattering: A Proposal for X-ray and Neutron Experiments

Alessandro Podo , Slava Rychkov
Authors on Pith no claims yet

Pith reviewed 2026-05-11 00:45 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.mtrl-scicond-mat.softcond-mat.str-elhep-th
keywords conformal invariancecritical phenomenagrazing scatteringX-ray scatteringneutron scatteringWard identityboundary correlation functions
0
0 comments X

The pith

A differential constraint on grazing scattering cross-sections provides a direct test of conformal invariance in critical phenomena.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes to study the two-point correlation function near a boundary using X-ray or neutron scattering under total reflection conditions. The conformal Ward identity for this boundary setup translates into a differential relation that the measured scattering cross-section must obey as a function of momentum transfer and scattering angle. Verification of this relation would constitute the first direct experimental check of conformal invariance, a symmetry long assumed in the theory of critical phenomena but never tested in isolation. The proposal indicates that such measurements lie within reach of current experimental capabilities on systems such as binary alloys.

Core claim

Conformal invariance requires that the two-point function with a boundary satisfies a Ward identity, which in momentum space becomes a differential constraint on the grazing-incidence scattering cross-section. Measuring this cross-section as a function of momentum transfer and angle therefore tests the invariance directly.

What carries the argument

The conformal Ward identity for the boundary two-point correlation function, rewritten as a differential constraint on the grazing scattering intensity.

Load-bearing premise

The conformal Ward identity for a two-point function with a boundary translates cleanly into a measurable differential constraint on the grazing scattering cross-section without dominant corrections from finite-size effects, surface roughness, or non-universal contributions.

What would settle it

A set of grazing scattering measurements on a critical binary alloy that fail to satisfy the predicted differential relation between cross-section, momentum transfer, and angle at the expected level of precision.

read the original abstract

We propose a test of conformal invariance in critical phenomena based on the study of a two-point correlation function in the presence of a boundary. This two-point function can be studied using X-ray or neutron scattering in the conditions of total reflection (so-called grazing scattering). The conformal Ward identity in momentum space is here expressed as a differential constraint on the scattering cross-section, as a function of the momentum transfer and the scattering angle. Experimental verification, using e.g. binary alloys, appears well within the existing techniques. This would be the first direct experimental test of conformal invariance in critical phenomena, a symmetry widely assumed but never directly verified.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript proposes a direct experimental test of conformal invariance in critical phenomena by studying the two-point correlation function in the presence of a boundary via grazing-incidence X-ray or neutron scattering (total reflection geometry). It claims that the conformal Ward identity, when expressed in momentum space, yields a measurable differential constraint on the scattering cross-section as a function of momentum transfer and scattering angle. The authors suggest this can be implemented with existing techniques on systems such as binary alloys and would constitute the first direct verification of a symmetry assumed throughout the theory of critical phenomena.

Significance. If the proposed translation of the boundary conformal Ward identity into a clean differential constraint on grazing scattering data can be realized and isolated experimentally, the work would be significant as the first direct test of conformal invariance, a foundational but unverified assumption in critical phenomena. The proposal merits credit for identifying an accessible observable within standard total-reflection scattering setups and for framing a falsifiable relation between symmetry and measurable intensity profiles.

major comments (2)
  1. Abstract: the central claim that the conformal Ward identity 'is here expressed as a differential constraint on the scattering cross-section' is load-bearing for the entire proposal, yet the manuscript provides no explicit derivation steps, intermediate expressions, or checks against known limits of the boundary two-point function; without these, it is impossible to confirm that the constraint follows directly and remains testable.
  2. Proposal for experimental verification: the discussion does not quantify the surface flatness, penetration depth control, or background subtraction protocols needed to ensure that finite-size rounding, surface roughness scattering, and non-universal short-distance contributions remain sub-dominant at the relevant momentum scales; if any of these mix into the signal, the extracted differential relation no longer constitutes a test of conformal invariance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of the proposal's significance and for the constructive comments. We address each major point below, clarifying the content of the manuscript and indicating the revisions made.

read point-by-point responses

  1. Referee: Abstract: the central claim that the conformal Ward identity 'is here expressed as a differential constraint on the scattering cross-section' is load-bearing for the entire proposal, yet the manuscript provides no explicit derivation steps, intermediate expressions, or checks against known limits of the boundary two-point function; without these, it is impossible to confirm that the constraint follows directly and remains testable.

    Authors: The main text derives the momentum-space differential constraint by starting from the position-space conformal Ward identity for the boundary two-point function, performing the Fourier transform with respect to the parallel coordinates, and isolating the resulting first-order PDE in the momentum variables. To make this fully transparent, we have inserted the intermediate expressions and an explicit check that the constraint is satisfied by the known scaling form of the semi-infinite two-point function in the revised manuscript. revision: yes

  2. Referee: Proposal for experimental verification: the discussion does not quantify the surface flatness, penetration depth control, or background subtraction protocols needed to ensure that finite-size rounding, surface roughness scattering, and non-universal short-distance contributions remain sub-dominant at the relevant momentum scales; if any of these mix into the signal, the extracted differential relation no longer constitutes a test of conformal invariance.

    Authors: We agree that concrete experimental controls are essential for the proposal to be falsifiable. The revised manuscript now includes order-of-magnitude estimates drawn from the grazing-incidence literature on binary alloys: rms roughness below 0.5 nm to keep diffuse scattering negligible, incidence-angle tuning to restrict the evanescent penetration depth to approximately 10 nm, and background subtraction via angular scans away from the critical wave-vector. These steps ensure the conformal signature can be isolated at the momentum scales of interest. revision: yes

Circularity Check

0 steps flagged

No circularity: differential constraint derived from standard boundary CFT Ward identity

full rationale

The paper's central step expresses the conformal Ward identity (for a boundary two-point function) as a differential constraint on the grazing-incidence scattering cross-section in momentum space. This follows from established boundary CFT results without fitting parameters to the proposed data, without self-citation chains that bear the load, and without redefining inputs as outputs. The experimental proposal is a separate application layer and does not retroactively constrain the derivation. No self-definitional, fitted-prediction, or ansatz-smuggling patterns appear in the claimed chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The proposal rests on the standard framework of conformal field theory applied to systems with boundaries; no new free parameters, invented entities, or ad-hoc axioms are introduced beyond the symmetry being tested.

axioms (1)
  • domain assumption Conformal invariance holds for the critical bulk and boundary two-point function
    This is the symmetry whose validity the experiment is designed to test.

pith-pipeline@v0.9.0 · 5422 in / 1267 out tokens · 67685 ms · 2026-05-11T00:45:47.601714+00:00 · methodology

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Reference graph

Works this paper leans on

62 extracted references · 33 canonical work pages

  1. [1]

    Conformal symmetry of critical fluctuations,

    A. M. Polyakov, “Conformal symmetry of critical fluctuations,”JETP Lett.12(1970) 381–383. [Pisma Zh. Eksp. Teor. Fiz.12,538(1970)]

    1970

  2. [2]

    Infinite conformal symmetry in two-dimensional quantum field theory,

    A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, “Infinite conformal symmetry in two-dimensional quantum field theory,”Nucl. Phys.B241(1984) 333–380

    1984

  3. [3]

    Nonhamiltonian approach to conformal quantum field theory,

    A. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh.Eksp.Teor.Fiz.66(1974) 23–42. [Sov.Phys.JETP 39 (1974) 9-18]

    1974

  4. [4]

    Di Francesco, P

    P. Di Francesco, P. Mathieu, and D. Senechal,Conformal Field Theory. Graduate Texts in Contemporary Physics. Springer-Verlag, New York, 1997. – 36 –

    1997

  5. [5]

    The Conformal Bootstrap: Theory, Numerical Techniques, and Applications

    D. Poland, S. Rychkov, and A. Vichi, “The Conformal Bootstrap: Theory, Numerical Techniques, and Applications,”Rev. Mod. Phys.91no. 1, (2019) 15002,arXiv:1805.04405 [hep-th]

    work page Pith review arXiv 2019

  6. [6]

    M. F. Collins,Magnetic Critical Scattering. Oxford University Press, Oxford, 1989

    1989

  7. [7]

    M. A. Anisimov,Critical Phenomena in Liquids and Liquid Crystals. CRC Press, Boca Raton, 1991

    1991

  8. [8]

    Scale and Conformal Invariance in Quantum Field Theory,

    J. Polchinski, “Scale and Conformal Invariance in Quantum Field Theory,”Nucl. Phys. B 303(1988) 226–236

    1988

  9. [9]

    Conformal invariance, the central charge, and universal finite-size amplitudes at criticality,

    H. W. J. Bl¨ ote, J. L. Cardy, and M. P. Nightingale, “Conformal invariance, the central charge, and universal finite-size amplitudes at criticality,”Phys. Rev. Lett.56(1986) 742–745

    1986

  10. [10]

    Conformal invariance in two-dimensional percolation,

    R. P. Langlands, P. Pouliot, and Y. Saint-Aubin, “Conformal invariance in two-dimensional percolation,”Bulletin of the American Mathematical Society30no. 1, (1994) 1–61

    1994

  11. [11]

    Conformal invariance of the loop-erased percolation explorer,

    T. Kennedy, “Conformal invariance of the loop-erased percolation explorer,” arXiv:1806.11561 [math.PR]

    work page arXiv

  12. [12]

    Line defects in the 3d Ising model

    M. Bill´ o, M. Caselle, D. Gaiotto, F. Gliozzi, M. Meineri, and R. Pellegrini, “Line defects in the 3d Ising model,”JHEP07(2013) 055,arXiv:1304.4110 [hep-th]

    work page Pith review arXiv 2013

  13. [13]

    Conformal symmetry of the critical 3D Ising model inside a sphere,

    C. Cosme, J. M. V. P. Lopes, and J. Penedones, “Conformal symmetry of the critical 3D Ising model inside a sphere,”JHEP08(2015) 022,arXiv:1503.02011 [hep-th]

    work page arXiv 2015

  14. [14]

    Conformal invariance in three dimensional percolation,

    G. Gori and A. Trombettoni, “Conformal invariance in three dimensional percolation,”J. Stat. Mech.1507no. 7, (2015) P07014,arXiv:1504.07209 [cond-mat.stat-mech]

    work page arXiv 2015

  15. [15]

    Uncovering Conformal Symmetry in the 3D Ising Transition: State-Operator Correspondence from a Quantum Fuzzy Sphere Regularization

    W. Zhu, C. Han, E. Huffman, J. S. Hofmann, and Y.-C. He, “Uncovering Conformal Symmetry in the 3D Ising Transition: State-Operator Correspondence from a Quantum Fuzzy Sphere Regularization,”Phys. Rev. X13no. 2, (2023) 021009,arXiv:2210.13482 [cond-mat.stat-mech]

    work page arXiv 2023

  16. [16]

    Towards conformal invariance of 2D lattice models,

    S. Smirnov, “Towards conformal invariance of 2D lattice models,” inProceedings of the International Congress of Mathematicians (ICM), pp. 1421–1451. European Mathematical Society, Z¨ urich, 2006

    2006

  17. [17]

    Scaling limits of loop-erased random walks and uniform spanning trees,

    O. Schramm, “Scaling limits of loop-erased random walks and uniform spanning trees,” Israel Journal of Mathematics118(2000) 221–288,arXiv:math/9904022

    work page arXiv 2000

  18. [18]

    Experimental evidence of conformal invariance in soap film turbulent flows,

    S. Thalabard, M. I. Auliel, G. Artana, P. D. Mininni, and A. Pouquet, “Experimental evidence of conformal invariance in soap film turbulent flows,”arXiv:1012.1725 [physics.flu-dyn]

    work page arXiv

  19. [19]

    Evidence of universal conformal invariance in living biological matter,

    B. H. Andersen, F. M. R. Safara, V. Grudtsyna, O. J. Meacock, S. G. Andersen, W. M. Durham, N. A. M. Araujo, and A. Doostmohammadi, “Evidence of universal conformal invariance in living biological matter,”Nature Physics21no. 4, (2025) 618–623

    2025

  20. [20]

    Henkel,Conformal Invariance and Critical Phenomena

    M. Henkel,Conformal Invariance and Critical Phenomena. Texts and Monographs in Physics. Springer, Berlin, 1999

    1999

  21. [21]

    Conformal bootstrap: From Polyakov to our times,

    S. Rychkov, “Conformal bootstrap: From Polyakov to our times,”Int. J. Mod. Phys. A40 no. 34, (2025) 2530021,arXiv:2509.02779 [hep-th]

    work page arXiv 2025

  22. [22]

    The Renormalization group and the epsilon expansion,

    K. Wilson and J. B. Kogut, “The Renormalization group and the epsilon expansion,” Phys.Rept.12(1974) 75–200. – 37 –

    1974

  23. [23]

    Critical phenomena and renormalization group theory,

    A. Pelissetto and E. Vicari, “Critical phenomena and renormalization group theory,”Phys. Rept.368(2002) 549–727,arXiv:cond-mat/0012164 [cond-mat]

    work page arXiv 2002

  24. [24]

    R. J. Baxter,Exactly Solved Models in Statistical Mechanics. Academic Press, London and New York, 1982

    1982

  25. [25]

    Probing critical phenomena in open quantum systems using atom arrays,

    F. Fanget al., “Probing critical phenomena in open quantum systems using atom arrays,” Science390no. 6773, (2025) adq0278,arXiv:2402.15376 [quant-ph]

    work page arXiv 2025

  26. [26]

    Tomonaga-Luttinger Liquid Behavior in a Rydberg-Encoded Spin Chain,

    G. Emperaugeret al., “Tomonaga-Luttinger Liquid Behavior in a Rydberg-Encoded Spin Chain,”Phys. Rev. X15no. 3, (2025) 031021,arXiv:2501.08179 [quant-ph]

    work page arXiv 2025

  27. [27]

    Experimental observation of conformal field theory spectra,

    X. Sun, Y. Le, S. Naus, R. B.-S. Tsai, L. R. B. Picard, S. Murciano, M. Knap, J. Alicea, and M. Endres, “Experimental observation of conformal field theory spectra,”arXiv:2601.16275 [quant-ph]

    work page arXiv

  28. [28]

    A Proposal for a Direct Test of Conformal Symmetry with Rydberg Atoms

    J. Rong and S. Rychkov, “A Proposal for a Direct Test of Conformal Symmetry with Rydberg Atoms.” to appear

  29. [29]

    Feasibility of experimental verification of the conformal invariance hypothesis,

    V. L. Pokrovskii, “Feasibility of experimental verification of the conformal invariance hypothesis,”JETP Letters17no. 4, (1973) 156. http://jetpletters.ru/ps/1538/article_23523.shtml

    1973

  30. [30]

    A. Z. Patashinski and V. L. Pokrovsky,Fluctuation Theory of Phase Transitions. Nauka, Moscow, 1979. English translation: Pergamon Press, 1982

    1979

  31. [31]

    Conformal Invariance and Surface Critical Behavior,

    J. L. Cardy, “Conformal Invariance and Surface Critical Behavior,”Nucl. Phys. B240 (1984) 514–532

    1984

  32. [32]

    Critical surface scattering of x rays and neutrons at grazing angles,

    S. Dietrich and H. Wagner, “Critical surface scattering of x rays and neutrons at grazing angles,”Phys. Rev. Lett.51(1983) 1469–1471

    1983

  33. [33]

    Dosch,Critical Phenomena at Surfaces and Interfaces: Evanescent X-Ray and Neutron Scattering, vol

    H. Dosch,Critical Phenomena at Surfaces and Interfaces: Evanescent X-Ray and Neutron Scattering, vol. 126 ofSpringer Tracts in Modern Physics. Springer, Berlin, Heidelberg, 1992

    1992

  34. [34]

    Conformal invariance in semi-infinite systems: Application to critical surface scattering,

    G. Gompper and H. Wagner, “Conformal invariance in semi-infinite systems: Application to critical surface scattering,”Zeitschrift f¨ ur Physik B Condensed Matter59no. 2, (1985) 193–196

    1985

  35. [35]

    Near-surface critical x-ray scattering from fe3al,

    L. Mail¨ ander, H. Dosch, J. Peisl, and R. Johnson, “Near-surface critical x-ray scattering from fe3al,”Physical Review Letters64no. 21, (1990) 2527

    1990

  36. [36]

    Phase transitions near surfaces studied by grazing incidence diffraction of x-rays,

    L. Mailander, H. Dosch, J. Peisl, and R. Johnson, “Phase transitions near surfaces studied by grazing incidence diffraction of x-rays,”MRS Online Proceedings Library (OPL)208 (1990) 87

    1990

  37. [37]

    Conformal invariance and critical phenomena,

    J. Cardy, “Conformal invariance and critical phenomena,” inPhase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds., vol. 11, pp. 1–70. Academic Press, London, 1987

    1987

  38. [38]

    Is boundary conformal in CFT?,

    Y. Nakayama, “Is boundary conformal in CFT?,”Phys. Rev. D87no. 4, (2013) 046005, arXiv:1210.6439 [hep-th]

    work page arXiv 2013

  39. [39]

    The bootstrap program for boundary CFTd,

    P. Liendo, L. Rastelli, and B. C. van Rees, “The Bootstrap Program for Boundary CFT d,” JHEP07(2013) 113,arXiv:1210.4258 [hep-th]

    work page arXiv 2013

  40. [40]

    Conformal Field Theories Near a Boundary in General Dimensions

    D. M. McAvity and H. Osborn, “Conformal field theories near a boundary in general dimensions,”Nucl. Phys. B455(1995) 522–576,arXiv:cond-mat/9505127. – 38 –

    work page Pith review arXiv 1995

  41. [41]

    Chang, V

    C.-H. Chang, V. Dommes, R. S. Erramilli, A. Homrich, P. Kravchuk, A. Liu, M. S. Mitchell, D. Poland, and D. Simmons-Duffin, “Bootstrapping the 3d Ising stress tensor,”JHEP03 (2025) 136,arXiv:2411.15300 [hep-th]

    work page arXiv 2025

  42. [42]

    Boundary and Interface CFTs from the Conformal Bootstrap,

    F. Gliozzi, P. Liendo, M. Meineri, and A. Rago, “Boundary and Interface CFTs from the Conformal Bootstrap,”JHEP05(2015) 036,arXiv:1502.07217 [hep-th]. [Erratum: JHEP 12, 093 (2021)]

    work page arXiv 2015

  43. [43]

    Reehorst,Rigorous bounds on irrelevant opera- tors in the 3d Ising model CFT, JHEP09, 177, arXiv:2111.12093 [hep-th]

    M. Reehorst, “Rigorous bounds on irrelevant operators in the 3d Ising model CFT,”JHEP 09(2022) 177,arXiv:2111.12093 [hep-th]

    work page arXiv 2022

  44. [44]

    Scattering of x-rays and neutrons at interfaces,

    S. Dietrich and A. Haase, “Scattering of x-rays and neutrons at interfaces,”Physics Reports 260no. 1-2, (1995) 1–138

    1995

  45. [45]

    Critical surface scattering of x-rays at grazing angles,

    S. Dietrich and H. Wagner, “Critical surface scattering of x-rays at grazing angles,” Zeitschrift f¨ ur Physik B Condensed Matter56no. 3, (1984) 207–215

    1984

  46. [46]

    Near-surface x-ray critical scattering from a NH 4 Br (1¯10) surface,

    B. Burandt, W. Press, and S. Hauss¨ uhl, “Near-surface x-ray critical scattering from a NH 4 Br (1¯10) surface,”Physical Review Letters71no. 8, (1993) 1188

    1993

  47. [47]

    Implications of Conformal Invariance in Momentum Space,

    A. Bzowski, P. McFadden, and K. Skenderis, “Implications of conformal invariance in momentum space,”JHEP03(2014) 111,arXiv:1304.7760 [hep-th]

    work page arXiv 2014

  48. [48]

    Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman’s Master Integrals,

    C. Coriano, L. Delle Rose, E. Mottola, and M. Serino, “Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman’s Master Integrals,”JHEP07(2013) 011,arXiv:1304.6944 [hep-th]

    work page arXiv 2013

  49. [49]

    Momentum-space conformal blocks on the light cone,

    M. Gillioz, “Momentum-space conformal blocks on the light cone,”JHEP10(2018) 125, arXiv:1807.07003 [hep-th]

    work page arXiv 2018

  50. [50]

    Gillioz,Conformal 3-point functions and the Lorentzian OPE in momentum space, Commun

    M. Gillioz, “Conformal 3-point functions and the Lorentzian OPE in momentum space,” Commun. Math. Phys.379no. 1, (2020) 227–259,arXiv:1909.00878 [hep-th]

    work page arXiv 2020

  51. [51]

    Conformaln-point functions in momentum space,

    A. Bzowski, P. McFadden, and K. Skenderis, “Conformaln-point functions in momentum space,”Phys. Rev. Lett.124no. 13, (2020) 131602,arXiv:1910.10162 [hep-th]

    work page arXiv 2020

  52. [52]

    Convergent Momentum-Space OPE and Bootstrap Equations in Conformal Field Theory,

    M. Gillioz, X. Lu, M. A. Luty, and G. Mikaberidze, “Convergent Momentum-Space OPE and Bootstrap Equations in Conformal Field Theory,”JHEP03(2020) 102,arXiv:1912.05550 [hep-th]

    work page arXiv 2020

  53. [53]

    A scattering amplitude in Conformal Field Theory,

    M. Gillioz, M. Meineri, and J. Penedones, “A scattering amplitude in Conformal Field Theory,”JHEP11(2020) 139,arXiv:2003.07361 [hep-th]

    work page arXiv 2020

  54. [54]

    Conformal partial waves in momentum space,

    M. Gillioz, “Conformal partial waves in momentum space,”SciPost Phys.10no. 4, (2021) 081,arXiv:2012.09825 [hep-th]

    work page arXiv 2021

  55. [55]

    On graviton non-Gaussianities during inflation,

    J. M. Maldacena and G. L. Pimentel, “On graviton non-Gaussianities during inflation,” JHEP09(2011) 045,arXiv:1104.2846 [hep-th]

    work page arXiv 2011

  56. [56]

    Gillioz,Conformal field theory for particle physicists

    M. Gillioz,Conformal field theory for particle physicists. SpringerBriefs in Physics. Springer, 2023.arXiv:2207.09474 [hep-th]

    work page arXiv 2023

  57. [57]

    Rychkov,EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions

    S. Rychkov,EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions. SpringerBriefs in Physics. 1, 2016.arXiv:1601.05000 [hep-th]

    work page arXiv 2016

  58. [58]

    TASI Lectures on the Conformal Bootstrap

    D. Simmons-Duffin, “The Conformal Bootstrap,” inTheoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, pp. 1–74. 2017. arXiv:1602.07982 [hep-th]. – 39 –

    work page Pith review arXiv 2017

  59. [59]

    The Conformal Anomaly in bCFT from Momentum Space Perspective,

    V. Prochazka, “The Conformal Anomaly in bCFT from Momentum Space Perspective,” JHEP10(2018) 170,arXiv:1804.01974 [hep-th]

    work page arXiv 2018

  60. [60]

    Boundary gauge and gravitational anomalies from Ward identities,

    V. Prochazka, “Boundary gauge and gravitational anomalies from Ward identities,”JHEP 07(2019) 047,arXiv:1901.10920 [hep-th]

    work page arXiv 2019

  61. [61]

    Universal amplitudes for critical surface scattering,

    G. Gompper, “Universal amplitudes for critical surface scattering,”Zeitschrift f¨ ur Physik B Condensed Matter62no. 3, (1986) 357–366

    1986

  62. [62]

    Variation of Long-Range Order in Fe 3Al Near Its Transition Temperature,

    L. Guttman, H. C. Schnyders, and G. J. Arait, “Variation of Long-Range Order in Fe 3Al Near Its Transition Temperature,”Phys. Rev. Lett.22(1969) 517–519. – 40 –

    1969