Derivation of effective field theories

TL;DR

This paper introduces a self-consistent cumulant expansion method to improve effective field theories, enabling systematic treatment of fluctuations and better understanding of phase transitions and ground state properties.

Contribution

It presents a novel approach extending mean-field theory with cumulant expansion for systematic fluctuation analysis and effective field theory development.

Findings

Calculated critical temperature and Landau parameters for $\

Analyzed fluctuation effects across different length scales.

Provided insights into ground state properties of many-body systems.

Abstract

A general self-consistency approach allows 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 new 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 new 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.