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

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 J1 and J2 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 J2/J1, 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 χ ∼ 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.