Abstract
We study the behaviour of a class of stochastic spatially extended systems exhibiting transition to absorbing configurations, reentrant noise induced phase transitions and phase transitions induced by noise crosscorrelations. We discuss the behaviour of the system in the presence of multiplicative fluctuations: a possibility of escaping from the absorbing state and the nature of disordered phase appearing beyond the second critical point of the reentrant phase transition. Making use of the mean field approach we have shown that noise cross-correlations lead to continuous, discontinuous and reentrant phase transitions.
Highlights
For the last three decades we have observed a considerable increase in the research of nonequilibrium phenomena in macroscopic systems for the purpose of explaining the constructive role of fluctuations of the environment in which the system is placed
A special type of behaviour of stochastic systems is observed in the case of several noise effects with cross-correlations leading to a remarkable and counterintuitive phenomena related to the transformation of phase transition type [10,11]
We focus on the effect of coloured fluctuations in order to investigate the system behaviour in the course of reentrant noise induced phase transition. Despite that, such transitions are characterized by two critical points, beyond the second critical point the system is determined to be in the disordered state
Summary
For the last three decades we have observed a considerable increase in the research of nonequilibrium phenomena in macroscopic systems for the purpose of explaining the constructive role of fluctuations of the environment in which the system is placed. Most popular of them are as follows: (i) the cumulant expansion method [5,4]; (ii) the spectral width expansion method [1,6]; (iii) the unified colored noise approximation [7,8] It appears that when the system is nonlinear, the spatial coupling and noise correlations force the system to exhibit a special behavior known as reentrant phase transition [8,9]. It will be shown that due to temporal correlations of the fluctuating sources one can define a discontinuous behavior of an order parameter To this end we explore an extended stochastic system that obeys the archetypical model of Brownian particle. Within the simplest model with drift caused by Landau-like potential and two colored (multiplicative and additive) noises, we illustrate that phase transitions of both continuous and discontinuous character are realized as biased phase transitions
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