Criticality in the two-dimensional random-bond Ising model

TL;DR

This paper investigates the critical properties of the 2D random-bond Ising model at a multicritical point, using network model mapping and numerical transfer matrix methods to estimate critical exponents.

Contribution

It introduces a novel approach to study the 2D random-bond Ising model's critical behavior by mapping it onto a network model and estimating critical exponents.

Findings

Critical exponents are estimated and found consistent with previous high-temperature series results.

The model exhibits a multicritical point on the phase boundary between ferromagnetic and paramagnetic phases.

The network model mapping reveals similarities and differences with quantum Hall transition models.

Abstract

The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both finite temperatures and disorder strength. We study the associated critical properties, by mapping the random 2D Ising model onto a network model. The model closely resembles network models of quantum Hall plateau transitions, but has different symmetries. Numerical transfer matrix calculations enable us to obtain estimates for the critical exponents at the random Ising phase transition. The values are consistent with recent estimates obtained from high-temperature series.