Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice

TL;DR

This study precisely locates the multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice and characterizes its critical behavior using finite-size scaling of Monte Carlo data.

Contribution

The paper provides the first high-precision determination of the Nishimori point and its critical exponents for the 2D +- J Ising model through extensive Monte Carlo simulations.

Findings

Nishimori point located at p^*=0.89081(7), T^*=0.9528(4)

Critical exponents y_1=0.655(15), y_2=0.250(2)

Thermal exponent u=4.00(3), crossover exponent =2.62(6)

Abstract

We investigate the critical behavior of the random-bond +- J Ising model on a square lattice at the multicritical Nishimori point in the T-p phase diagram, where T is the temperature and p is the disorder parameter (p=1 corresponds to the pure Ising model). We perform a finite-size scaling analysis of high-statistics Monte Carlo simulations along the Nishimori line defined by $2p-1={\rm Tanh}(1/T)$, along which the multicritical point lies. The multicritical Nishimori point is located at p^*=0.89081(7), T^*=0.9528(4), and the renormalization-group dimensions of the operators that control the multicritical behavior are y_1=0.655(15) and y_2 = 0.250(2); they correspond to the thermal exponent \nu= 1/y_2=4.00(3) and to the crossover exponent \phi= y_1/y_2=2.62(6).