Critical and multicritical behavior of the +- J Ising model in two and three dimensions

TL;DR

This study uses Monte Carlo simulations to analyze the critical and multicritical behavior of the +- J Ising model in two and three dimensions, revealing universality classes and the nature of disorder effects.

Contribution

The paper provides the first comprehensive numerical analysis of the multicritical Nishimori point and critical behavior in both two and three dimensions of the +- J Ising model.

Findings

In 3D, the critical behavior matches the randomly dilute Ising universality class.

In 2D, the critical behavior is governed by the pure Ising fixed point with logarithmic corrections.

The multicritical Nishimori point's location and RG dimensions are precisely determined.

Abstract

We report our Monte Carlo results on the critical and multicritical behavior of the +- J Ising model [with a random-exchange probability P(J_{xy}) = p \delta(J_{xy} - J) + (1-p) \delta(J_{xy} + J)], in two and three dimensions. We study the transition line between the paramagnetic and ferromagnetic phase, which extends from p=1 to a multicritical (Nishimori) point. By a finite-size scaling analysis, we provide strong numerical evidence that in three dimensions the critical behavior along this line belongs to the same universality class as that of the critical transition in the randomly dilute Ising model. In two dimensions we confirm that the critical behavior is controlled by the pure Ising fixed point and that disorder is marginally irrelevant, giving rise to universal logarithmic corrections. In both two and three dimensions, we also determine the location of the multicritical Nishimori point, as well as the renormalization-group dimensions of the operators that control the renormalization-group flow close to it.