Coleman-Weinberg Phase Transition in Two-Scalar Models

TL;DR

This paper investigates the nature of the Coleman-Weinberg phase transition in a two-scalar field model beyond perturbation theory, revealing a rich phase diagram with first and second order transitions separated by a triple point.

Contribution

It provides a non-perturbative analysis of the phase transition in a two-scalar model using flow equations, extending understanding beyond standard perturbative methods.

Findings

Identifies regions with first and second order phase transitions.

Establishes a phase diagram with a triple point.

Quantitative agreement with perturbative Coleman-Weinberg results.

Abstract

We explore the Coleman-Weinberg phase transition in regions outside the validity of perturbation theory. For this purpose we study a Euclidean field theory with two scalars and discrete symmetry in four dimensions. The phase diagram is established by a numerical solution of a suitable truncation of exact non-perturbative flow equations. We find regions in parameter space where the phase transition (in dependence on the mass term) is of the second or the first order, separated by a triple point. Our quantitative results for the first order phase transition compare well to the standard perturbative Coleman-Weinberg calculation of the effective potential.