Strong disorder fixed points in the two-dimensional random-bond Ising model

TL;DR

This study investigates the critical points of the 2D random-bond Ising model using numerical methods, revealing distinct universality classes and the re-entrant nature of the paramagnetic phase.

Contribution

It provides a detailed numerical analysis of various fixed points in the 2D random-bond Ising model, confirming universality of the Nishimori point and identifying distinct universality classes.

Findings

Nishimori point is universal across disorder types.

Different fixed points belong to separate universality classes.

Paramagnetic phase is re-entrant below the Nishimori point.

Abstract

The random-bond Ising model on the square lattice has several disordered critical points, depending on the probability distribution of the bonds. There are a finite-temperature multicritical point, called Nishimori point, and a zero-temperature fixed point, for both a binary distribution where the coupling constants take the values +/- J and a Gaussian disorder distribution. Inclusion of dilution in the +/- J distribution (J=0 for some bonds) gives rise to another zero-temperature fixed point which can be identified with percolation in the non-frustrated case (J >= 0). We study these fixed points using numerical (transfer matrix) methods. We determine the location, critical exponents, and central charge of the different fixed points and study the spin-spin correlation functions. Our main findings are the following: (1) We confirm that the Nishimori point is universal with respect to the type of disorder, i.e. we obtain the same central charge and critical exponents for the +/- J and Gaussian distributions of disorder. (2) The Nishimori point, the zero-temperature fixed point for the +/- J and Gaussian distributions of disorder, and the percolation point in the diluted case all belong to mutually distinct universality classes. (3) The paramagnetic phase is re-entrant below the Nishimori point, i.e. the zero-temperature fixed points are not located exactly below the Nishimori point, neither for the +/- J distribution, nor for the Gaussian distribution.