Nonequilibrium critical dynamics of the relaxational models C and D

TL;DR

This paper studies the nonequilibrium critical dynamics of models C and D, revealing conditions under which genuine nonequilibrium fixed points emerge or are suppressed, with implications for dynamic scaling and critical exponents.

Contribution

It provides a detailed analysis of nonequilibrium effects on models C and D, identifying new fixed points and scaling behaviors, especially for n=2 and n=3.

Findings

For n=1, no genuine nonequilibrium fixed point; behavior similar to equilibrium.

For n=2 and 3, lines of nonequilibrium fixed points with varying exponents emerge.

Anisotropic noise leads to different critical behaviors and long-range interactions.

Abstract

We investigate the critical dynamics of the $n$-component relaxational models C and D which incorporate the coupling of a nonconserved and conserved order parameter S, respectively, to the conserved energy density rho, under nonequilibrium conditions by means of the dynamical renormalization group. Detailed balance violations can be implemented isotropically by allowing for different effective temperatures for the heat baths coupling to the slow modes. In the case of model D with conserved order parameter, the energy density fluctuations can be integrated out. For model C with scalar order parameter, in equilibrium governed by strong dynamic scaling (z_S = z_rho), we find no genuine nonequilibrium fixed point. The nonequilibrium critical dynamics of model C with n = 1 thus follows the behavior of other systems with nonconserved order parameter wherein detailed balance becomes effectively restored at the phase transition. For n >= 4, the energy density decouples from the order parameter. However, for n = 2 and n = 3, in the weak dynamic scaling regime (z_S <= z_rho) entire lines of genuine nonequilibrium model C fixed points emerge to one-loop order, which are characterized by continuously varying critical exponents. Similarly, the nonequilibrium model C with spatially anisotropic noise and n < 4 allows for continuously varying exponents, yet with strong dynamic scaling. Subjecting model D to anisotropic nonequilibrium perturbations leads to genuinely different critical behavior with softening only in subsectors of momentum space and correspondingly anisotropic scaling exponents. Similar to the two-temperature model B the effective theory at criticality can be cast into an equilibrium model D dynamics, albeit incorporating long-range interactions of the uniaxial dipolar type.