High-temperature expansion methods for Ising systems with quenched impurities

Abstract

Two methods are used to obtain high-temperature series for Ising systems with quenched randomness. One is a direct averaging of a linked-cluster expansion, the other combines the primitive high-temperature expansion and the Edward replica trick. After a bond renormalization, the second expansion is seen to be identical to the first term by term. The series are developed for the case of a spin-glass model in which the bonds have a probability which is symmetrically distributed about zero. Specifically, series for the free energy and appropriately chosen susceptibility are given to 11th and 10th orders, respectively, for a hypercubic lattice in any dimension and for any symmetrical bond distribution.