First order and critical point phase transitions in cooperative assemblies with many-body interactions: some exact results

Abstract

The complete thermodynamics of a model hamiltonian with general-spin infinite range Ising 2-point, 4-point,... interaction terms is found exactly in two different statistical mechanical ensembles which prove to be essentially equivalent. The coefficients of the above terms may be chosen to give critical behaviour which is largely consistent with the idea of scaling and which has delta equal to any odd positive integer and gamma =1; alternatively a first order phase transition may be obtained, a finite spontaneous magnetization appearing as the temperature is decreased through that of the transition. The Heisenberg case is also considered and found to be closely similar to the Ising case.