Phase transitions induced by noise cross-correlations

Dmitrii Kharchenko

Sumy State University, Modeling of Complex Systems Dept., Sumy, Ukraine

A general approach for treating the spatially extended stochastic systems with the nonlinear damping and correlations between additive and multiplicative noises is developed. Within the modified cumulant expansion method, we derive an effective Fokker--Planck equation with stationary solutions that describe the character of the ordered state. We find that the fluctuation cross--correlations lead to a symmetry breaking of the distribution function even in the case of zero--dimensional system. In general case, continuous, discontinuous and reentrant noise induced phase transitions take place. It appears that the cross--correlations play the role of bias field which can induce a chain of phase transitions of different nature. Within the mean field approach, we give an intuitive explanation of the system behavior by an effective potential of the thermodynamic type. This potential is written in the form of an expansion with coefficients defined by the temperature, intensity of spatial coupling, auto- and cross--correlation times and intensities of both additive and multiplicative noises.

The above formalism is applied to investigate statistical properties of three-component synergetic system of Lorenz type allowing to describe a picture of phase transitions in self-consistent manner. The model is considered in the framework of adiabatic elimination procedure. Such a kind of assumption allows to represent a behavior of the system described by slow variables (order parameter and conjugate field) where additive noises are transformed to multiplicative ones. It is shown that in the case of slow variation of the order parameter the system undergoes reentrant phase transition with a variation of additive noise autocorrelation time. In the case of both additive and multiplicative noises being uncorrelated the system becomes ordered in standard manner. If above noises are correlated then the picture of phase transition is more complicated as introduced above.

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