Critical behaviour of a modified spherical model

Abstract

A class of models with spherical constraints is considered. The critical temperatures for a particular case are obtained numerically and are found to depend on a model parameter alpha contrary to a conjecture of Barrett and Kac (1975). Under certain assumptions, the critical exponents are related to those of an auxiliary model which would have the Ising-like behaviour when alpha >0 under the universality assumption. Also, the usual spherical model ( alpha =0) results are reproduced from this approach.