Upper bounds to the zero-field susceptibilities and magnetisations for the random-bound Ising model and the random-bond n-vector model

Abstract

The self-avoiding walk approximation is used to give upper bounds to the zero-field spin-pair correlation function, zero-field susceptibilities and the spontaneous magnetisation for the systems of the random-bond Ising model of general spin S and the random-bond n-vector model, where the exchange integrals are assumed to be random variables. Using these bounds, the authors find a sufficient condition for the disappearance of the long-range orders. The condition is stronger for some cases than the one obtained previously by the authors. The present one applies to some cases for which the preceding one does not.