High-Temperature Series Analysis of the Free Energy and Susceptibility of the 2D Random-Bond Ising Model

TL;DR

This study uses high-temperature series expansions to analyze the critical behavior of the 2D random-bond Ising model, revealing evidence for a specific susceptibility singularity and exploring disorder effects.

Contribution

It provides the first detailed high-temperature series analysis of the 2D random-bond Ising model's free energy and susceptibility across various disorder strengths.

Findings

Susceptibility exhibits a singularity consistent with theoretical predictions.

Results support the predicted form of the susceptibility divergence.

Specific heat results are less conclusive but align with theoretical expectations.

Abstract

We derive high-temperature series expansions for the free energy and susceptibility of the two-dimensional random-bond Ising model with a symmetric bimodal distribution of two positive coupling strengths J_1 and J_2 and study the influence of the quenched, random bond-disorder on the critical behavior of the model. By analysing the series expansions over a wide range of coupling ratios J_2/J_1, covering the crossover from weak to strong disorder, we obtain for the susceptibility with two different methods compelling evidence for a singularity of the form $\chi \sim t^{-7/4} |\ln t|^{7/8}$, as predicted theoretically by Shalaev, Shankar, and Ludwig. For the specific heat our results are less convincing, but still compatible with the theoretically predicted log-log singularity.