Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model

TL;DR

This study investigates the ground-state properties of the 2D random-bond Ising model, revealing a reentrant phase diagram and no evidence of spin-glass order at finite temperature, using an exact matching algorithm for large systems.

Contribution

The paper introduces an exact matching algorithm enabling large-scale analysis of the 2D random-bond Ising model's ground states, uncovering a reentrant phase diagram and absence of spin-glass order.

Findings

Paramagnet-ferromagnet transition at p_c ~ 0.103

Reentrant phase diagram with transition at p_n ~ 0.109

No evidence of spin-glass ordering at finite temperature

Abstract

We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration $p\in[0,1]$ of antiferromagnetic and $(1-p)$ of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension $L$ up to 700. We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at $p_c \sim 0.103$ compared to the concentration $p_n\sim 0.109$ at the Nishimory point, which means that the phase diagram of the model exhibits a reentrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.