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High-temperature series analysis of the free energy and susceptibility of the 2D random-bond Ising model


  • Roder, Alexandra
  • Adler, Joan
  • Janke, Wolfhard


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|lnt|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.

Suggested Citation

  • Roder, Alexandra & Adler, Joan & Janke, Wolfhard, 1999. "High-temperature series analysis of the free energy and susceptibility of the 2D random-bond Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(1), pages 28-42.
  • Handle: RePEc:eee:phsmap:v:265:y:1999:i:1:p:28-42
    DOI: 10.1016/S0378-4371(98)00481-6

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