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The free energy at T = 0 of the spin glass in the case of the continuous distribution of the effective field on the Bethe lattice for Z = 4, 5, 6

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  • Akagi, Eiichi
  • Seino, Mitsuhiro
  • Katsura, Shigetoshi

Abstract

We evaluated the free energy at T = 0 of the ±J random Ising model on the Bethe lattice of the coordination number z = 4, 5, 6 in the case where the distribution function of the effective field has a continuous distribution, by using the method of the integral equation of the effective field.

Suggested Citation

  • Akagi, Eiichi & Seino, Mitsuhiro & Katsura, Shigetoshi, 1991. "The free energy at T = 0 of the spin glass in the case of the continuous distribution of the effective field on the Bethe lattice for Z = 4, 5, 6," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(3), pages 406-414.
    • Handle: RePEc:eee:phsmap:v:178:y:1991:i:3:p:406-414
    DOI: 10.1016/0378-4371(91)90029-C
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    1. Gebauer, Rolf H, 1987. "Socio-economic Classification of Farm Households--Conceptual, Methodological and Empirical Considerations," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 14(3), pages 261-283.
    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.
    3. Seino, Mitsuhiro & Katsura, Shigetoshi, 1990. "The energy of the spin glass with the continuous distribution of the effective field at T=0," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(2), pages 781-788.
    4. 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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