Thermodynamics of an Ising model with random exchange interactions

Abstract

An Ising model with an arbitrary distribution $P(J)$ of exchange interactions $J$ is solved exactly for the annealed case in which the system is allowed to reach complete thermal equilibrium at each temperature. The solution is expressed in terms of an Ising model on the same lattice with a single exchange parameter, allowing an exact solution to be obtained in one and two dimensions. Some feeling for the effect of annealing can be found by examining correlations between exchange interactions on neighboring bonds. Some special distributions $P(J)$ are examined in detail.