Wilson Renormalization Group Study of Inverse Symmetry Breaking

TL;DR

This paper uses Wilson renormalization group methods to study inverse symmetry breaking at high temperatures in field theories, confirming the phenomenon's robustness beyond perturbation theory.

Contribution

It demonstrates that inverse symmetry breaking persists beyond loop expansion estimates using a non-perturbative RG approach, clarifying its physical relevance.

Findings

Inverse symmetry breaking occurs in the studied model.

The parameter space volume for inverse phase structure matches perturbative predictions.

Coupling constants run according to one-loop beta functions at high temperature.

Abstract

For a large class of field theories there exist portions of parameter space for which the loop expansion predicts increased symmetry breaking at high temperature. Even though this behavior would clearly have far reaching implications for cosmology such theories have not been fully investigated in the literature. This is at least partially due to the counter intuitive nature of the result, which has led to speculations that it is merely an artifact of perturbation theory. To address this issue we study the simplest model displaying high temperature symmetry breaking using a Wilson renormalization group approach. We find that although the critical temperature is not reliably estimated by the loop expansion the total volume of parameter space which leads to the inverse phase structure is not significantly different from the perturbative prediction. We also investigate the temperature dependence of the coupling constants and find that they run approximately according to their one-loop $\beta$-functions at high temperature. Thus, in particular, the quartic coupling of $phi^4$ theory is shown to increase with temperature, in contrast to the behavior obtained in some previous studies.