Out-of-equilibrium critical dynamics of the three-dimensional ${\mathbb Z}_2$ gauge model along critical relaxational flows

TL;DR

This paper investigates the out-of-equilibrium critical dynamics of the 3D ${ m Z}_2$ gauge model after quenches to the critical point, using finite-size scaling to accurately determine the dynamic critical exponent.

Contribution

It introduces a finite-size scaling approach to analyze out-of-equilibrium dynamics in lattice gauge theories and provides a precise measurement of the dynamic critical exponent $z$.

Findings

Dynamic critical exponent $z=2.610(15)$ obtained.

Out-of-equilibrium finite-size scaling framework developed.

Improved accuracy over previous equilibrium-based estimates.

Abstract

We address the out-of-equilibrium critical dynamics of the three-dimensional lattice ${\mathbb Z}_2$ gauge model, and in particular the critical relaxational flows arising from instantaneous quenches to the critical point, driven by purely relaxational (single-spin-flip Metropolis) upgradings of the link ${\mathbb Z}_2$ gauge variables. We monitor the critical relaxational dynamics by computing the energy density, which is the simplest local gauge-invariant quantity that can be measured in a lattice gauge theory. The critical relaxational flow of the three-dimensional lattice ${\mathbb Z}_2$ gauge model is analyzed within an out-of-equilibrium finite-size scaling framework, which allows us to compute the dynamic critical exponent $z$ associated with the purely relaxational dynamics of the three-dimensional ${\mathbb Z}_2$ gauge universality class. We obtain $z=2.610(15)$, which significantly improves earlier results obtained by other methods, in particular those obtained by analyzing the equilibrium critical dynamics.