High Temperature Phase Transitions in Two-Scalar Theories with Large $N$ Techniques

TL;DR

This paper uses large N techniques to analyze phase transitions in a two-scalar field theory at high temperatures, revealing the nature of the transitions through effective potential calculations.

Contribution

It introduces a large N approach to compute the effective potential and study phase transitions in a coupled scalar field model at finite temperature.

Findings

Identification of first and second order phase transitions

Effective potential resummation of infinite graph subclasses

Temperature dependence of scalar field expectation value

Abstract

We consider a theory of a scalar one-component field $\phi$ coupled to a scalar $N$-component field $\chi$. Using large $N$ techiques we calculate the effective potential in the leading order in $1/N$. We show that this is equivalent to a resummation of an infinite subclass of graphs in perturbation theory, which involve fluctuations of the $\chi$ field only. We study the temperature dependence of the expectation value of the $\phi$ field and the resulting first and second order phase transitions.