A disordered ising model with internal degrees of freedom

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=_i>₀²/N, which is not necessarily the order parameter of the basic system, is different from zero (q0) forT_c. The whole system consists of the basis {S_i} and an equal number of additional spins _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–_i can be interpreted as clusters with an internal degree of freedom. The specific heat c and the susceptibility of the internal degree of freedom can be separated exactly and show typical spin glass properties: the specific heat c is an analytic function over the whole temperature range and the susceptibility shows a cusp at the transition temperatureT_c of the basic system.