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Ising spin glass in the Bethe approximation at zero temperature

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  • de Oliveira, M.J.

Abstract

We study the properties of the Ising spin glass in the Bethe approximation at zero temperature for the case of a ±J distribution of bonds. We show that there is an infinite number of solutions for the probability distribution function of the effective field. Each one is a sum of 2N+1 delta functions located at Jn/N, n=0,±1, ±2,…,±N. In the limit N→∞ we obtain a solution with a continous part in addition to delta functions located at 0 and ±J. For each case we calculate the spin glass order parameter, the energy and entropy.

Suggested Citation

  • de Oliveira, M.J., 1988. "Ising spin glass in the Bethe approximation at zero temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 148(3), pages 567-574.
    • Handle: RePEc:eee:phsmap:v:148:y:1988:i:3:p:567-574
    DOI: 10.1016/0378-4371(88)90087-8
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    1. 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.
    2. Kirkpatrick, Jeane, 1975. "Representation in the American National Conventions: the Case of 1972," British Journal of Political Science, Cambridge University Press, vol. 5(3), pages 265-322, July.
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