Continuous universality in nonequilibrium relaxational dynamics of O(2) symmetric systems

Abstract

We elucidate a nonconserved relaxational nonequilibrium dynamics of a O(2) symmetric model. We drive the system out of equilibrium by introducing a nonzero noise cross correlation of amplitude D(×) in a stochastic Langevin description of the system, while maintaining the O(2) symmetry of the order parameter space. By performing dynamic renormalization group calculations in a field-theoretic set up, we analyze the ensuing nonequilibrium steady states and evaluate the scaling exponents near the critical point, which now depend explicitly on D(×). Since the latter remains unrenormalized, we obtain universality classes varying continuously with D(×). More interestingly, by changing D(×) continuously from zero, we can make our system move away from its equilibrium behavior (i.e., when D(×)=0) continuously and incrementally.

Active to absorbing state phase transition in the presence of a fluctuating environment: feedback and universality

“…Thus, this study is substantially different from and complementary to Ref. [9] in having an environment dynamics that is no longer autonomous due to the feedback, a situation not considered in Ref. [9].…”

“…[9] in having an environment dynamics that is no longer autonomous due to the feedback, a situation not considered in Ref. [9]. Apart from the consideration of the feedback of φ on the dynamics of the environment, we point out a crucial technical difference that the environmental dynamics has a short-ranged Gaussian noise (see below), unlike in Ref.…”

“…Nonetheless, it is reasonable to expect that environmental fluctuations should affect the universal scaling properties of the AAPT in the DP universality class. For instance, the critical scaling behaviour of a density φ undergoing an AAPT in the presence of fluctuating environments has been shown in [9]; see also [10,11] for related studies. In [9] different models were used to describe the fluctuating environments namely (i) the randomly stirred fluid modeled by the Navier-Stokes equation and (ii) fluctuating surface modelled by the Kardar-Parisi-Zhang equation or (iii) the Edward-Wilkinson equation.…”

“…For instance, the critical scaling behaviour of a density φ undergoing an AAPT in the presence of fluctuating environments has been shown in [9]; see also [10,11] for related studies. In [9] different models were used to describe the fluctuating environments namely (i) the randomly stirred fluid modeled by the Navier-Stokes equation and (ii) fluctuating surface modelled by the Kardar-Parisi-Zhang equation or (iii) the Edward-Wilkinson equation. In all these cases the dynamic exponent of the environment was found to be either same as the DP dynamic exponent (strong dynamic scaling) or different from that of the dynamic exponent of the percolating field (weak dynamic scaling) resulting in non DP behaviour.…”

“…Apart from the consideration of the feedback of φ on the dynamics of the environment, we point out a crucial technical difference that the environmental dynamics has a short-ranged Gaussian noise (see below), unlike in Ref. [9], where the corresponding noises are all considered to be spatially long-ranged. Our principal result here is that the scaling behaviour of the system near the extinction transition of the AAPT is, in general, affected by the feedback on the environment and hence non-DP like.…”