Phase Transitions out of Equilibrium: domain formation and growth

TL;DR

This paper investigates the non-equilibrium dynamics of phase transitions in scalar field theories, focusing on domain formation and growth after rapid supercooling, using a non-perturbative approach to reveal how domain size evolves over time.

Contribution

It introduces a non-perturbative Hartree approximation to study domain growth during out-of-equilibrium phase transitions in scalar fields, highlighting the dependence on coupling strength.

Findings

Domain size grows as rac12;t at long times.

Weakly coupled theories produce larger final domains than strongly coupled ones.

Transition speed correlates with the coupling strength, with faster transitions in strongly coupled theories.

Abstract

We study the dynamics of phase transitions out of equilibrium in weakly coupled scalar field theories. We consider the case in which there is a rapid supercooling from an initial symmetric phase in thermal equilibrium at temperature $T_i>T_c$ to a final state at low temperature $T_f \approx 0$. In particular we study the formation and growth of correlated domains out of equilibrium. It is shown that the dynamics of the process of domain formation and growth (spinodal decomposition) cannot be studied in perturbation theory, and a non-perturbative self-consistent Hartree approximation is used to study the long time evolution. We find in weakly coupled theories that the size of domains grow at long times as $\xi_D(t) \approx \sqrt{t\xi(0)}$. For very weakly coupled theories, their final size is several times the zero temperature correlation length. For strongly coupled theories the final size of the domains is comparable to the zero temperature correlation length and the transition proceeds faster.