Conformal perturbation of off-critical correlators in the 3D Ising universality class

TL;DR

This paper uses conformal bootstrap data to accurately estimate off-critical correlators in the 3D Ising universality class through conformal perturbation theory, matching simulations and experiments.

Contribution

It introduces a method to compute off-critical correlators in 3D Ising using conformal bootstrap data and perturbation theory, providing high-precision results.

Findings

Agreement with Monte Carlo simulations

Consistency with experimental estimates

Precise evaluation of leading and next-to-leading terms

Abstract

Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and OPE coefficients for several 3D universality classes. We show how to use this information to obtain similarly precise estimates for off-critical correlators using conformal perturbation. We discuss in particular the $< \sigma (r) \sigma (0) >$, $< \epsilon (r) \epsilon (0) >$ and $< \sigma (r) \epsilon (0) >$ two point functions in the high and low temperature regimes of the 3D Ising model and evaluate the leading and next to leading terms in the $s = t r^{\Delta_{t}}$ expansion, where $t$ is the reduced temperature. Our results for $< \sigma (r) \sigma (0) >$ agree both with Monte Carlo simulations and with a set of experimental estimates of the critical scattering function.