Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators

TL;DR

This paper introduces a numerical method to determine Operator Product Expansion (OPE) coefficients in 3D Conformal Field Theories by analyzing off-critical correlators, successfully applied to the 3D Ising model.

Contribution

The authors propose a novel numerical approach for extracting OPE coefficients from off-critical correlators, validated on the 3D Ising model, providing new data for bootstrap constraints.

Findings

Estimated C^{σ}_{σϵ} = 1.07(3), consistent with bootstrap results.

Estimated C^{ε}_{εε} = 1.45(30), a new result for the 3D Ising model.

Method offers a new way to analyze conformal data near criticality.

Abstract

We propose a general method for the numerical evaluation of OPE coefficients in three dimensional Conformal Field Theories based on the study of the conformal perturbation of two point functions in the vicinity of the critical point. We test our proposal in the three dimensional Ising Model, looking at the magnetic perturbation of the $<\sigma (\mathbf {r})\sigma(0)>$, $<\sigma (\mathbf {r})\epsilon(0)>$ and $<\epsilon (\mathbf {r})\epsilon(0)>$ correlators from which we extract the values of $C^{\sigma}_{\sigma\epsilon}=1.07(3)$ and $C^{\epsilon}_{\epsilon\epsilon}=1.45(30)$. Our estimate for $C^{\sigma}_{\sigma\epsilon}$ agrees with those recently obtained using conformal bootstrap methods, while $C^{\epsilon}_{\epsilon\epsilon}$, as far as we know, is new and could be used to further constrain conformal bootstrap analyses of the 3d Ising universality class.