Eur. Phys. J. B 7, 309-330 (1999)
https://doi.org/10.1007/s100510050617

Non-equilibrium critical behavior of O(n)-symmetric systems^*

Effect of reversible mode-coupling terms and dynamical anisotropy

¹ Institut für Theoretische Physik, Technische Universität München, James-Franck-Straße, 85747 Garching, Germany
² Institute for Theoretical Physics, Eötvös University, 1088 Budapest, Puskin u. 5-7, Hungary and Department of Physics -Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK

Received: 17 July 1998
Accepted: 25 August 1998
Published online: 15 January 1999

Abstract

Phase transitions in non-equilibrium steady states of O(n)-symmetric models with reversible mode couplings are studied using dynamic field theory and the renormalization group. The systems are driven out of equilibrium by dynamical anisotropy in the noise for the conserved quantities, i.e., by constraining their diffusive dynamics to be at different temperatures and in - and -dimensional subspaces, respectively. In the case of the Sasvári-Schwabl-Szépfalusy (SSS) model for planar ferro- and isotropic antiferromagnets, we assume a dynamical anisotropy in the noise for the non-critical conserved quantities that are dynamically coupled to the non-conserved order parameter. We find the equilibrium fixed point (with isotropic noise) to be stable with respect to these non-equilibrium perturbations, and the familiar equilibrium exponents therefore describe the asymptotic static and dynamic critical behavior. Novel critical features are only found in extreme limits, where the ratio of the effective noise temperatures is either zero or infinite. On the other hand, for model J for isotropic ferromagnets with a conserved order parameter, the dynamical noise anisotropy induces effective long-range elastic forces, which lead to a softening only of the -dimensional sector in wavevector space with lower noise temperature . The ensuing static and dynamic critical behavior is described by power laws of a hitherto unidentified universality class, which, however, is not accessible by perturbational means for . We obtain formal expressions for the novel critical exponents in a double expansion about the static and dynamic upper critical dimensions and , i.e., about the equilibrium theory.