Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1802.07157

Comment on "A structural test for the conformal invariance of the critical 3d Ising model" by S. Meneses, S. Rychkov, J. M. Viana Parente Lopes and P. Yvernay. arXiv:1802.02319

Bertrand Delamotte, Matthieu Tissier, Nicolás Wschebor

Published Feb 20, 2018• 0 citations
arXivHTMLPDF

Abstract

In a recent preprint [ArXiv 1802.02319], Meneses et al. challenge our proof that scale invariance implies conformal invariance for the three-dimensional Ising model [B. Delamotte, M. Tissier and N. Wschebor, Phys. Rev. E 93 (2016), 012144.]. We refute their arguments. We also point out a mistake in their one-loop calculation of the dimension of the vector operator $V_μ$ of lowest dimension which is not a total derivative.

DOI
10.48550/arxiv.1802.07157

Related papers

A structural test for the conformal invariance of the critical 3d Ising model

Simão M. João, João Penedones, Slava Rychkov +2 more

Abstract How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current — a non-conserved vector operator of dimension exactly (d − 1), whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound Δ V > 5.0 on the scaling dimension of the lowest virial current candidate V, well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model.

arXiv:1802.02319•Journal of High Energy Physics•Apr 1, 2019•17 citations

Comment on “Critical point scaling of Ising spin glasses in a magnetic field”

T. Temesvári

In a section of a recent paper [Phys. Rev. B 91, 104432 (2015)], the authors discuss some of the arguments in the paper by Parisi and Temesv\'ari [Nucl. Phys. B 858, 293 (2012)]. In this Comment, it is shown how these arguments are misinterpreted and the existence of the Almeida-Thouless transition $\mathit{in}$ the upper critical dimension six reasserted.

arXiv:1610.04747•Physical review. B./Physical review. B•Nov 1, 2016•3 citations

Comment on a recent conjectured solution of the three-dimensional Ising model arXiv:0705.1045

Fa Yueh Wu, Barry M. McCoy, Michael Ellis Fisher +1 more

In a recent paper published in the Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87, 5309-5419 (2007), arXiv:0705.1045], the author advances a conjectured solution for various properties of the three-dimensional Ising model. Here we disprove the conjecture and point out the flaws in the arguments leading to the conjectured expressions.

arXiv:0811.3876•Nov 24, 2008•4 citations

Scale invariance implies conformal invariance for the three-dimensional Ising model

Bertrand Delamotte, Matthieu Tissier, Nicolás Wschebor

Using the Wilson renormalization group, we show that if no integrated vector operator of scaling dimension -1 exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that scale invariance implies conformal invariance for the three-dimensional Ising model.

arXiv:1501.01776•Physical review. E•Jan 25, 2016•42 citations

Comment on ‘Mathematical structure of the three-dimensional (3D) Ising model’∗

Jacques H. H. Perk

The review paper by Zhang Zhi-Dong (Zhang Z D 2013 Chin. Phys. B 22 030513, arXiv:1305.2956) contains many errors and is based on several earlier works that are equally wrong.

•Jan 1, 2013•13 citations

Comment on ‘Mathematical structure of the three-dimensional (3D) Ising model’

Jacques H. H. Perk

The review paper by Zhang Zhi-Dong (Zhang Z D 2013 Chin. Phys. B 22 030513 , arXiv:1305.2956) contains many errors and is based on several earlier works that are equally wrong.

arXiv:1307.1753•Chinese Physics B•Aug 1, 2013•13 citations
In a recent preprint [ArXiv 1802.02319], Meneses et al. challenge our proof that scale invariance implies conformal invariance for the three-dimensional Ising model [B. Delamotte, M. Tissier and N. Wschebor, Phys. Rev. E 93 (2016), 012144.]. We refute their arguments. We also point out a mistake in their one-loop calculation of the dimension of the vector operator VμV_μVμ​ of lowest dimension which is not a total derivative.
Abstract How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current — a non-conserved vector operator of dimension exactly (d − 1), whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound Δ V > 5.0 on the scaling dimension of the lowest virial current candidate V, well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model.
In a section of a recent paper [Phys. Rev. B 91, 104432 (2015)], the authors discuss some of the arguments in the paper by Parisi and Temesv\'ari [Nucl. Phys. B 858, 293 (2012)]. In this Comment, it is shown how these arguments are misinterpreted and the existence of the Almeida-Thouless transition in\mathit{in}in the upper critical dimension six reasserted.