High Temperature Expansion Study of the Nishimori multicritical Point in Two and Four Dimensions

TL;DR

This paper investigates the Nishimori multicritical point in 2D and 4D using high temperature expansions, estimating critical exponents and comparing them to percolation results, revealing similarities in 2D and differences in 4D.

Contribution

It provides new estimates of critical exponents at the Nishimori multicritical point in 2D and 4D, highlighting their relation to percolation theory.

Findings

2D exponents close to percolation values

3D exponents similar to percolation

4D exponents differ significantly from percolation

Abstract

We study the two and four dimensional Nishimori multicritical point via high temperature expansions for the $\pm J$ distribution, random-bond, Ising model. In $2d$ we estimate the the critical exponents along the Nishimori line to be $\gamma=2.37\pm 0.05$, $\nu=1.32\pm 0.08$. These, and earlier $3d$ estimates $\gamma =1.80\pm 0.15$, $\nu=0.85\pm 0.08$ are remarkably close to the critical exponents for percolation, which are known to be $\gamma=43/18$, $\nu=4/3$ in $d=2$ and $\gamma=1.805\pm0.02$ and $\nu=0.875\pm 0.008$ in $d=3$. However, the estimated $4d$ Nishimori exponents $\gamma=1.80\pm 0.15$, $\nu=1.0\pm 0.1$, are quite distinct from the $4d$ percolation results $\gamma=1.435\pm 0.015$, $\nu=0.678\pm 0.05$.