Continuous Universality in non-equilibrium relaxational dynamics of O(2) symmetric systems

TL;DR

This paper investigates how introducing a non-zero noise cross-correlation in an O(2) symmetric model leads to continuously varying universality classes in non-equilibrium steady states, analyzed through dynamic renormalization group methods.

Contribution

It demonstrates that non-zero noise cross-correlation induces a continuum of universality classes in non-equilibrium O(2) systems, with critical exponents depending explicitly on the cross-correlation amplitude.

Findings

Universality classes vary continuously with noise cross-correlation D_x.

Critical exponents depend explicitly on D_x.

System transitions smoothly from equilibrium to non-equilibrium behavior.

Abstract

We elucidate a non-conserved relaxational nonequilibrium dynamics of a O(2) symmetric model. We drive the system out of equilibrium by introducing a non-zero noise cross-correlation of amplitude $D_\times$ in a stochastic Langevin description of the system, while maintaining the O(2) symmetry of the order parameter space. By performing dynamic renormalization group calculations in a field-theoretic set up, we analyze the ensuing nonequilibrium steady states and evaluate the scaling exponents near the critical point, which now depend explicitly on $D_\times$. Since the latter remains unrenormalized, we obtain universality classes varying continuously with $D_\times$. More interestingly, by changing $D_\times$ continuously from zero, we can make our system move away from its equilibrium behavior (i.e., when $D_\times=0$) continuously and incrementally.