Nonequilibrium critical dynamics of the relaxational models C and D

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 ρ, 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, leaving no trace of the nonequilibrium perturbations in the asymptotic regime. For model C with scalar order parameter, in equilibrium governed by strong dynamic scaling (z_S = z_ρ), we find no genuine nonequilibrium fixed point either. 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 generally decouples from the order parameter. However, for n = 2 and n = 3, in the weak dynamic scaling regime (z_S ≤ z_ρ) entire lines of genuine nonequilibrium model C fixed points emerge to one-loop order, which are characterized by continuously varying static and dynamic 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 (randomly driven diffusive systems) the effective theory at criticality can be cast into an equilibrium model D dynamics, albeit incorporating long-range interactions of the uniaxial dipolar or ferroelastic type.