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Spin-glass and ferromagnetic phases of the random-bond Ising model on the Bethe lattice

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  • Morita, T.

Abstract

Magnetic properties are numerically obtained for the random-bond Ising model of interactions + J (J > 0) and - J with probabilities p(p ⩾/ 0.5) and 1 − p, on the Bethe lattice of coordination number 3 in zero and non-zero uniform external magnetic fields. It is confirmed that the phase transitions between the ferromagnetic, the paramagnetic and the spin-glass phase occur under zero or infinitesimal uniform external field. The phase boundary between the ferromagnetic and the spin-glass phase is determined. It is shown that the susceptibility does not diverge but only has a cusp at this phase transition. The critical concentration pc at zero temperature is 0.86940 ± 0.00003. Evidence is given to show that the self-consistent solution of the effective field becomes unstable at the phase boundaries. No phase transition is found in a non-zero external field. It is concluded that the entropy and the specific heat in the Bethe approximation in the spin-glass phase are non-negative and the entropy tends to zero as the temperature approaches zero.

Suggested Citation

  • Morita, T., 1984. "Spin-glass and ferromagnetic phases of the random-bond Ising model on the Bethe lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(2), pages 321-343.
  • Handle: RePEc:eee:phsmap:v:125:y:1984:i:2:p:321-343
    DOI: 10.1016/0378-4371(84)90058-X
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    References listed on IDEAS

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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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