Reentrant transitions in the van Hemmen model of a spin glass

Abstract

The van Hemmen model of a spin glass, which is an Ising model with random couplings J ij between sites i and j equal to J 0 + J(ξ i η j + ξ j η i ), where (ξ i , η i ) are independent, identically distributed random variables, is studied in the pair approximation of the cluster variation method. For the family of probability distributions 1 2 (1 − p)δ(ξ i − a) + pδ(ξ i ) + 1 2 (1 − p)δ(ξ i + a), where p is varied, phase diagrams are constructed. They are qualitatively different from the mean-field phase diagrams and display a competition between tendencies towards spin-glass and towards ferromagnetic ordering, which results in reentrant transitions. It is argued that the observed effects are not accidental but are borne by the competition of bonds of the underlying lattice system.