Non-equilibrium scaling across first-order transitions with relativistic scalar fields

TL;DR

This study explores the out-of-equilibrium dynamics of a relativistic scalar field theory during first-order phase transitions, revealing universal scaling behaviors and crossovers between mean-field, Kibble-Zurek, and nucleation-dominated regimes.

Contribution

It demonstrates that universal non-equilibrium scaling can be observed across first-order transitions with relativistic fields, identifying conditions for different dynamical regimes and their scaling functions.

Findings

Fast driving induces temperature- and dimension-independent finite-time scaling.

Near $T_c$, a crossover from mean-field to Kibble-Zurek scaling occurs.

At low temperatures, nucleation and growth dominate, causing scaling corrections.

Abstract

We investigate the out-of-equilibrium dynamics of a relativistic $Z_2$-symmetric scalar field theory with Langevin dynamics in two and three spatial dimensions under linear driving across magnetic first-order phase transitions, close to and far below the critical temperature $T_c$. Using classical-statistical lattice simulations, we find that if the driving timescale is sufficiently fast, the system exhibits finite-time scaling behavior independent of temperature and dimensionality, identical to that observed in mean-field simulations. In slow quenches near $T_c$ this mean-field behavior crosses over to critical Kibble-Zurek scaling behavior, while for temperatures $T \ll T_c$ nucleation and growth dominate the transition dynamics, resulting in corrections to scaling. Near the transition point where the order parameter changes sign, the crossover between mean-field and critical out-of-equilibrium dynamics is found to be well described by the leading algebraic correction to Kibble-Zurek scaling. We find that universal non-equilibrium scaling behavior can be observed for $T \lesssim T_c$, provided the driving is fast enough to avoid nucleation but slow enough for correlations to form, and compute the associated universal scaling functions for the order parameter.