Derivation of effective field theories

Abstract

A general self-consistency approach allows for a thorough treatment of the corrections to the mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a point of view on the effective field theories. The proposed approach can be used for a systematic treatment of fluctuation effects of various length scales and, perhaps, for the development of a coarse-graining procedure. We outline and justify our method by some preliminary calculations. Results are given for the critical temperature and the Landau parameters of the phi(4) theory--the field counterpart of the Ising model. An important unresolved problem of the modern theory of phase transitions--the problem for the calculation of the true critical temperature--is considered within the framework of the present approach. A comprehensive description of the ground-state properties of many-body systems is also demonstrated.