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

T. Morita

Physica A: Statistical Mechanics and its Applications, 1984, vol. 125, issue 2, 321-343

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.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:125:y:1984:i:2:p:321-343

DOI: 10.1016/0378-4371(84)90058-X

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