The Exact Renormalization Group and First-Order Phase Transitions

TL;DR

This paper reviews the use of the exact renormalization group to study first-order phase transitions, focusing on universal critical behavior and bubble-nucleation rate calculations.

Contribution

It provides a comprehensive review of applying the exact renormalization group to analyze first-order phase transitions and nucleation rates, highlighting recent methodological advances.

Findings

Universal critical behavior near weakly first-order transitions analyzed.

Application of the exact renormalization group to bubble-nucleation rates discussed.

Assessment of homogeneous nucleation theory's reliability included.

Abstract

Studies of first-order phase transitions through the use of the exact renormalization group are reviewed. In the first part the emphasis is on universal aspects: We discuss the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields -- the cubic anisotropy model. In the second part we review the application of the exact renormalization group to the calculation of bubble-nucleation rates. More specifically, we concentrate on the pre-exponential factor. We discuss the reliability of homogeneous nucleation theory that employs a saddle-point expansion around the critical bubble for the calculation of the nucleation rate.