Critical Behavior of O(n)-symmetric Systems With Reversible Mode-coupling Terms: Stability Against Detailed-balance Violation

TL;DR

This paper studies the critical behavior of O(n)-symmetric systems with reversible mode-coupling under nonequilibrium conditions, finding new unstable fixed points but ultimately restoring equilibrium properties near criticality.

Contribution

It introduces a nonequilibrium variant of an O(n) model with detailed-balance violation and analyzes its critical fixed points using renormalization group methods.

Findings

Two new fixed points identified at different temperature ratios.

Both fixed points are unstable, leading to equilibrium behavior near criticality.

Restoration of equilibrium static and dynamic properties at the critical point.

Abstract

We investigate nonequilibrium critical properties of $O(n)$-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasv\'ari, Schwabl, and Sz\'epfalusy is studied, where violation of detailed balance is incorporated by allowing the order parameter and the dynamically coupled conserved quantities to be governed by heat baths of different temperatures $T_S$ and $T_M$, respectively. Dynamic perturbation theory and the field-theoretic renormalization group are applied to one-loop order, and yield two new fixed points in addition to the equilibrium ones. The first one corresponds to $\Theta = T_S / T_M = \infty$ and leads to model A critical behavior for the order parameter and to anomalous noise correlations for the generalized angular momenta; the second one is at $\Theta = 0$ and is characterized by mean-field behavior of the conserved quantities, by a dynamic exponent $z = d / 2$ equal to that of the equilibrium SSS model, and by modified static critical exponents. However, both these new fixed points are unstable, and upon approaching the critical point detailed balance is restored, and the equilibrium static and dynamic critical properties are recovered.