A disordered ising model with internal degrees of freedom

Abstract

A solvable Ising-system withnn-interactions as a basic system is considered. This system is assumed to undergo a phase transition so that the thermal quantityq=Σ<S _i> ²₀ /N, which is not necessarily the order parameter of the basic system, is different from zero (q≠0) forT<T _c. The whole system consists of the basis {S _i} and an equal number of additional spins η _i which are coupled linearly with the basic spinsS _i through an exchange constantJ _i which is distributed at random. The pairs of spinsS _i −η _i can be interpreted as clusters with an internal degree of freedom. The specific heat Δc and the susceptibility Δ_χ of the internal degree of freedom can be separated exactly and show typical spin glass properties: the specific heat Δc is an analytic function over the whole temperature range and the susceptibility Δ_χ shows a cusp at the transition temperatureT _c of the basic system.