Critical Ising Model in Varying Dimension by Conformal Bootstrap
Abstract
The single-correlator conformal bootstrap is solved numerically for several values of dimension 4>d>2 using the available SDPB and Extremal Functional methods. Critical exponents and other conformal data of low-lying states are obtained over the entire range of dimensions with up to four-decimal precision and then compared with several existing results. The conformal dimensions of leading-twist fields are also determined up to high spin, and their d-dependence shows how the conformal states rearrange themselves around d=2.2 for matching the Virasoro conformal blocks in the d=2 limit. The decoupling of states at the Ising point is studied for 3>d>2 and the vanishing of one structure constant at d=3 is found to persist till d=2 where it corresponds to a Virasoro null-vector condition.
Cite
@article{arxiv.1811.07751,
title = {Critical Ising Model in Varying Dimension by Conformal Bootstrap},
author = {Andrea Cappelli and Lorenzo Maffi and Satoshi Okuda},
journal= {arXiv preprint arXiv:1811.07751},
year = {2019}
}
Comments
43 pages, 15 figures, 7 tables, numerical data and Mathematica files are available upon request; v2: epsilon-expansion data added