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
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.
PACS: 05.70.Ln – Non-equilibrium thermodynamics, irreversible processes / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 64.60.Ht – Dynamic critical phenomena
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999