Second-order phase transitions in a non-equilibrium liquid-gas model withreversible mode couplings, i.e., model H for binary-fluid critical dynamics,are studied using dynamic field theory and the renormalization group. Thesystem is driven out of equilibrium either by considering different values forthe noise strengths in the Langevin equations describing the evolution of thedynamic variables (effectively placing these at different temperatures), ormore generally by allowing for anisotropic noise strengths, i.e., byconstraining the dynamics to be at different temperatures in d_par- andd_perp-dimensional subspaces, respectively. In the first, case, we find oneinfrared-stable and one unstable renormalization group fixed point. At thestable fixed point, detailed balance is dynamically restored, with the twonoise strengths becoming asymptotically equal. The ensuing critical behavior isthat of the standard equilibrium model H. At the novel unstable fixed point,the temperature ratio for the dynamic variables is renormalized to infinity,resulting in an effective decoupling between the two modes. We compute thecritical exponents at this new fixed point to one-loop order. For model H withspatially anisotropic noise, we observe a critical softening only in thed_perp-dimensional sector in wave vector space with lower noise temperature.The ensuing effective two-temperature model H does not have any stable fixedpoint in any physical dimension, at least to one-loop order. We obtain formalexpressions for the novel critical exponents in a double expansion about theupper critical dimension d_c = 4 - d_par and with respect to d_par, i.e., aboutthe equilibrium theory.
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