Non-gaussianity of the critical 3d Ising model

TL;DR

This paper analyzes the non-gaussian features of the critical 3d Ising model's four-point function using conformal bootstrap results, revealing significant non-gaussianity constrained by theoretical inequalities.

Contribution

It provides the first detailed analysis of the non-gaussianity ratio in the critical 3d Ising model based on bootstrap data, confirming theoretical bounds.

Findings

The four-point function shows significant non-gaussianity.

The ratio Q is constrained between 1/3 and 1.

Results are consistent with Lebowitz and Aizenman's inequality.

Abstract

We discuss the 4pt function of the critical 3d Ising model, extracted from recent conformal bootstrap results. We focus on the non-gaussianity Q - the ratio of the 4pt function to its gaussian part given by three Wick contractions. This ratio reveals significant non-gaussianity of the critical fluctuations. The bootstrap results are consistent with a rigorous inequality due to Lebowitz and Aizenman, which limits Q to lie between 1/3 and 1.