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3D Ising CFT and Exact Diagonalization on Icosahedron: The Power of Conformal Perturbation Theory
by Bing-Xin Lao, Slava Rychkov
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Slava Rychkov |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2307.02540v3 (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 |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
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.
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.
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.
Published as SciPost Phys. 15, 243 (2023)