Bethe Approximation for a Random Mixture of a Quenched Ising Ferro and Antiferromagnet

Abstract

A Bethe approximation for the phase transition in a quenched random Ising lattice is developed on the basis of the ordered phases with non-periodic spin arrangements. Mixtures of ferro and antiferromagnetic interactions are specially interested. The effects due to the interaction loops, which are characteristic to a ordinary lattice in contrast to a cayley tree on the transition temperature are stressed. Matsubara and Sakata’s results are critically compared with ours.