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3D Ising CFT and Exact Diagonalization on Icosahedron: The Power of Conformal Perturbation Theory

by Bing-Xin Lao, Slava Rychkov

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Submission summary

Authors (as registered SciPost users): Slava Rychkov
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-11-29
Date submitted: 2023-11-20 15:10
Submitted by: Rychkov, Slava
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


We consider the transverse field Ising model in $(2+1)$D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a meaningful comparison to the 3D Ising CFT on $\mathbb{R}\times S^2$, by including effective perturbations of the CFT Hamiltonian with a handful of local operators. This extreme example shows the power of conformal perturbation theory in understanding finite $N$ effects in models on regularized $S^2$. Its ideal arena of application should be the recently proposed models of fuzzy sphere regularization.

Published as SciPost Phys. 15, 243 (2023)

Author comments upon resubmission

We thank both referees for their reports. We corrected the typos they noticed, thanks, and tried to address the comments (except for inverting the blue and red colors in Fig.1 - but we do agree that in other contexts predominance of blue would be greatly desirable).

The new footnote 7 hopefully addresses the request of Report 1 about derivatives of a primary in the tau direction. We also followed the advice of Report 1 and augmented the title to better reflect the scope of our work.

The new footnotes 1 and 4 hopefully address comments 1) and 2) of Report 2.

Submission & Refereeing History

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Resubmission 2307.02540v3 on 20 November 2023

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