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

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

1999-05-18

arxiv.org/abs/cond-mat/9905255v1

Physics

Condensed Matter

19 pages, 6 Postscript figures

Scientific paper

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.

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