  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 T^\par and T^\perp in
d_\par- and d_\perp-dimensional subspaces, respectively. In the case of the
Sasv'ari-Schwabl-Sz'epfalusy (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 T^\par/T^\perp 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 d_\perp-dimensional sector in wavevector space
with lower noise temperature T^\perp < T^\par. 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 d_\par \geq 1. We obtain formal expressions for the novel critical
exponents in a double expansion about the static and dynamic upper critical
dimensions and d_\par, i.e., about the equilibrium theory.
