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We investigate nonequilibrium critical properties of $O(n)$-symmetric modelswith reversible mode-coupling terms. Specifically, a variant of the model ofSasv\'ari, Schwabl, and Sz\'epfalusy is studied, where violation of detailedbalance is incorporated by allowing the order parameter and the dynamicallycoupled conserved quantities to be governed by heat baths of differenttemperatures $T_S$ and $T_M$, respectively. Dynamic perturbation theory and thefield-theoretic renormalization group are applied to one-loop order, and yieldtwo new fixed points in addition to the equilibrium ones. The first onecorresponds to $\Theta = T_S / T_M = \infty$ and leads to model A criticalbehavior for the order parameter and to anomalous noise correlations for thegeneralized angular momenta; the second one is at $\Theta = 0$ and ischaracterized by mean-field behavior of the conserved quantities, by a dynamicexponent $z = d / 2$ equal to that of the equilibrium SSS model, and bymodified static critical exponents. However, both these new fixed points areunstable, and upon approaching the critical point detailed balance is restored,and the equilibrium static and dynamic critical properties are recovered.Comment: 18 pages, RevTeX, 1 figure included as eps-file; submitted to Phys.  Rev.

Critical behavior of O(n)-symmetric systems with reversible mode-coupling terms: Stability against detailed-balance violation