Self-consistent treatment of a phase transition

A self-consistent treatment of a phase transition with a scalar order parameter in the ordered and disordered state is described. The factorization of the correlation functions in the disordered phase leads to a shift of the transition temperature, a linear divergence (=1) for the correlation length, a quadratic divergence (=2) for the susceptibility, and a finite value (=–1) for the specific heat. In the ordered phase the factorization of the correlation functions leads to no divergences in the correlation length and susceptibility. A study of the free energy shows that order persists above the transition temperature found by assuming disorder. The requirement of thermodynamic stability induces a first-order transition at a temperature which lies between the bare transition temperature and the shifted one.Supported in part by NSF grant No-GP-17560.This work is in partial fulfillment of Ph.D. requirements at Brandeis University.