Modeling Thermal Fluctuations: Phase Mixing and Percolation

TL;DR

This paper models the nonequilibrium dynamics of a scalar field in a double-well potential, analyzing phase mixing and percolation driven by thermal fluctuations and domain instability.

Contribution

It introduces an analytical model based on subcritical bubbles to quantify phase fluctuations and links symmetry restoration to percolation phenomena.

Findings

Quantitative agreement with numerical simulations.

Phase mixing correlates with percolation driven by domain instability.

Model applicable to systems in the Ising universality class.

Abstract

We consider the nonequilibrium dynamics of a a real scalar field in a degenerate double-well potential. The system is prepared in the lowest free energy state in one of the wells and the dynamics is driven by the coupling of the field to a thermal bath. Using a simple analytical model, based on the subcritical bubbles method, we compute the fraction of the total volume which fluctuates to the opposite phase as a function of the parameters of the potential. Furthermore, we show how complete phase mixing, {\em i.e.} symmetry restoration, is related to percolation, which is dynamically driven by domain instability. Our method describes quantitatively recent results obtained by numerical simulations, and is applicable to systems in the Ising universality class.