Non-gaussianity of the critical 3d Ising model

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.

Figures (6)

• Figure 1: $Q$ in critical 3d Ising, plotted in region $R$.
• Figure 2: $Q$ in critical 2d Ising, plotted in region $R$.
• Figure 3: An example of a closed graph $\eta$.
• Figure 4: An example of a closed current corresponding to the closed HT graph from Fig. \ref{['fig-HT']}. Only the bonds for which $\mathbf{n}(b)\ne0$ are shown. According to the definition in the text, $\mathbf{n}$ connects vertices $A,B$ but not $A,C$ or $A,D$.
• Figure 5: A current $\mathbf{m}$ with $\partial \mathbf{m}=\{1,2,3,4\}$ (left) and the corresponding graph ${\cal M}$ (right).