SciPost Submission Page
3D Ising CFT and Exact Diagonalization on Icosahedron: The Power of Conformal Perturbation Theory
by Bing-Xin Lao, Slava Rychkov
Submission summary
| Authors (as registered SciPost users): | Slava Rychkov |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2307.02540v3 (pdf) |
| Date accepted: | Nov. 29, 2023 |
| Date submitted: | Nov. 20, 2023, 3:10 p.m. |
| Submitted by: | Slava Rychkov |
| 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
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.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)