The Effective Potential for Composite Operator in the Scalar Model at Finite Temperature

TL;DR

This paper develops a non-perturbative approach using the composite operator method to analyze the effective potential in scalar $\

Contribution

It extends the composite operator method to finite temperature scalar field theories, providing resummed effective potentials in D=3 and D=4.

Findings

Derived the finite temperature effective potential using the $1/N$ expansion.

Analyzed the phase structure of the scalar models at finite temperature.

Provided explicit forms of the effective potential in D=3 and D=4.

Abstract

We discuss the $\phi^4$ and $\phi^6$ theory defined in a flat $D$-dimensional space-time. We assume that the system is in equilibrium with a thermal bath at temperature $\beta^{-1}$. To obtain non-perturbative result, the $ 1/N $ expansion is used. The method of the composite operator (CJT) for summing a large set of Feynman graphs, is developed for the finite temperature system. The ressumed effective potential and the analysis of the D=3 and D=4 cases are given.