Thermal phase mixing during first-order phase transitions

Abstract

The dynamics of first-order phase transitions are studied in the context of (3+1)-dimensional scalar field theories. Particular attention is paid to the question of quantifying the strength of the transition, and how ``weak'' and ``strong'' transitions have different dynamics. We propose a model with two available low temperature phases separated by an energy barrier so that one of them becomes metastable below the critical temperature ${\mathit{T}}_{\mathit{c}}$. The system is initially prepared in this phase and is coupled to a thermal bath. Investigating the system at its critical temperature we find that ``strong'' transitions are characterized by the system remaining localized within its initial phase, while ``weak'' transitions are characterized by considerable phase mixing. Always at ${\mathit{T}}_{\mathit{c}}$, we argue that the two regimes are themselves separated by a (second-order) phase transition, with order parameter given by the equilibrium fractional population difference between the two phases and control parameter given by the strength of the scalar field's quartic self-coupling constant. We obtain a Ginzburg-like criterion to distinguish between ``weak'' and ``strong'' transitions, in agreement with previous results in 2+1 dimensions.