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On the bethe approximation for the random bond Ising model

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  • Horiguchi, Tsuyoshi

Abstract

A random bond Ising model is considered in terms of the pair approximation, which is equivalent to the Bethe approximation, of the cluster variation method. On taking the configurational average over the random distribution of bonds ±J, we take into account the nearest neighbor correlations between effective fields and bonds. We investigate their effects to the phase transition temperature from the paramagnetic phase to the ferro- (or antiferro-) magnetic phase and to the spin glass phase for the Ising model on the square lattice. It turns out that the correlation effects act favorably to the spin glass phase and bend upward the line of transition temperature from the paramagnetic phase to the spin glass phase as the concentration being apart from 0.5. In the appendix, we derive the expression of free energy in the weak interaction limit.

Suggested Citation

  • Horiguchi, Tsuyoshi, 1981. "On the bethe approximation for the random bond Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 107(2), pages 360-370.
    • Handle: RePEc:eee:phsmap:v:107:y:1981:i:2:p:360-370
    DOI: 10.1016/0378-4371(81)90095-9
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    1. N. Shukla, 1979. "Estimation of a regression coefficient after two preliminary tests of significance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 26(1), pages 183-193, December.
    2. Katsura, Shigetoshi & Inawashiro, Sakari & Fujiki, Sumiyoshi, 1979. "Spin glasses for the infinitely long ranged bond Ising model and for the short ranged binary bond Ising model without use of the replica method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 99(1), pages 193-216.
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