Precision Islands in the Ising and $O(N)$ Models

TL;DR

This paper uses conformal bootstrap with mixed correlators to precisely determine scaling dimensions and OPE coefficients in 3d Ising and $O(N)$ models, improving accuracy over previous studies.

Contribution

It introduces a method that scans over OPE coefficient ratios, incorporating physical constraints to achieve more precise conformal data for 3d models.

Findings

Most precise scaling dimensions and OPE coefficients for 3d Ising model.

Enhanced bootstrap method with mixed correlators and coefficient ratio scanning.

Quantitative results for key operators in 3d Ising and $O(N)$ models.

Abstract

We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, $O(2)$, and $O(3)$ models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a single operator at a given scaling dimension. The scaling dimensions and OPE coefficients obtained for the 3d Ising model, $(\Delta_{\sigma}, \Delta_{\epsilon},\lambda_{\sigma\sigma\epsilon}, \lambda_{\epsilon\epsilon\epsilon}) = (0.5181489(10), 1.412625(10), 1.0518537(41), 1.532435(19))$, give the most precise determinations of these quantities to date.