OPE Coefficients of the 3D Ising model with a trapping potential

TL;DR

This paper demonstrates a novel method to compute OPE coefficients in the 3D Ising model using a trapping potential, extending previous techniques and confirming known results with improved accuracy.

Contribution

It introduces a new approach combining trap size scaling with conformal perturbation to estimate OPE coefficients in the 3D Ising model.

Findings

Estimated $C^{\sigma}_{\sigma\e}= 1.051(3)$ consistent with literature

Estimated $C^{\e}_{\e\e}= 1.32(15)$ improves previous bounds

Method applicable to non-uniform perturbations in critical models

Abstract

Recently the OPE coefficients of the 3D Ising model universality class have been calculated by studying the two-point functions perturbed from the critical point with a relevant field. We show that this method can be applied also when the perturbation is performed with a relevant field coupled to a non uniform potential acting as a trap. This setting is described by the trap size scaling ansatz, that can be combined with the general framework of the conformal perturbation in order to write down the correlators $<\sigma (\mathbf {r})\sigma(0)>$, $<\sigma (\mathbf{r})\epsilon(0)>$ and $<\epsilon (\mathbf {r})\epsilon(0)>$, from which the OPE coefficients can be estimated. We find $C^{\sigma}_{\sigma\epsilon}= 1.051(3)$ , in agreement with the results already known in the literature, and $C^{\epsilon}_{\epsilon\epsilon}= 1.32 (15)$ , confirming and improving the previous estimate obtained in the uniform perturbation case.