Universal non-equilibrium scaling of cumulants across a critical point

TL;DR

This paper investigates the universal non-equilibrium behavior of a scalar field theory near a critical point, using lattice simulations to measure cumulants and scaling functions during a quench, revealing universal scaling laws and finite-size effects.

Contribution

It provides the first comprehensive computation of non-equilibrium cumulant scaling functions for a Model A universality class system during a quench.

Findings

Universal non-equilibrium scaling functions of cumulants up to fourth order.

Good data collapse onto universal finite-size scaling functions.

Extension of Kibble-Zurek theory to include higher-order cumulants.

Abstract

We study the critical dynamics of a scalar field theory with $Z_2$ symmetry in the dynamic universality class of Model A in two and three spatial dimensions with classical-statistical lattice simulations. In particular, we measure the non-equilibrium behavior of the system under a quench protocol in which the symmetry-breaking external field is changed at a constant rate through the critical point. Using the well-established Kibble-Zurek scaling theory we compute non-equilibrium scaling functions of cumulants of the order parameter up to fourth order. Together with the static critical exponents and the dynamic critical exponent, these fully describe the universal non-equilibrium evolution of the system near the critical point. We further extend the analysis to include finite-size effects and observe good collapse of our data onto two-dimensional universal non-equilibrium and finite-size scaling functions.