Disordering effects of color in nonequilibrium phase transitions induced by multiplicative noise

We introduce a class of exactly solvable models which exhibit an ordering noise-induced phase transition driven by an entropic mechanism. In contrast with previous studies, order does not appear in this case as a result of an instability of the disordered phase produced by noise, but of a balance between the relaxing deterministic dynamics and the randomizing (entropic) character of the fluctuations. A finite-size scaling analysis of the phase transition reveals that it belon...

The noise power spectra of spatially extended dynamical systems are investigated, using as a model the Complex Ginzburg-Landau equation with a stochastic term. Analytical and numerical investigations show that the spatial spectra of the ordered state are similar to Bose-Einstein distribution, showing 1/k^2 asymptotics in the long wavelength limit. The temporal noise spectra of the ordered state are obtained of 1/^alpha form, where alpha=2-D/2 with D the spatial dimension of t...

For phase transitions in disordered systems, an exact theorem provides a bound on the finite size correlation length exponent: \nu_{FS}<= 2/d. It is believed that the true critical exponent \nu of a disorder induced phase transition satisfies the same bound. We argue that in disordered systems the standard averaging introduces a noise, and a corresponding new diverging length scale, characterized by \nu_{FS}=2/d. This length scale, however, is independent of the system's own ...

In this paper we present a general result with an easily checkable condition that ensures a transition from chaotic regime to regular regime in random dynamical systems with additive noise. We show how this result applies to a prototypical family of nonuniformly expanding one dimensional dynamical systems, showing the main mathematical phenomenon behind Noise Induced Order. Accepted at Journal of Statistical Physics

We present a path integral formalism to compute potentials for nonequilibrium steady states, reached by a multiplicative stochastic dynamics. We develop a weak-noise expansion, which allows the explicit evaluation of the potential in arbitrary dimensions and for any stochastic prescription. We apply this general formalism to study noise-induced phase transitions. We focus on a class of multiplicative stochastic lattice models and compute the steady state phase diagram in term...

We study the flocking and pattern formations of active particles with a Vicsek-like model that includes a configuration dependent noise term. In particular, we couple the strength of the noise with both the local density and orientation of neighboring particles. Our results show that such a configuration dependent noise can lead to the appearance of large-scale ordered and disordered patterns, without the need for any complex alignment interactions. In particular, we obtain a...

We investigate the influence of time-varying environmental noise, i.e., temporal disorder, on the nonequilibrium phase transition of the contact process. Combining a real-time renormalization group, scaling theory, and large scale Monte-Carlo simulations in one and two dimensions, we show that the temporal disorder gives rise to an exotic critical point. At criticality, the effective noise amplitude diverges with increasing time scale, and the probability distribution of the ...

Active particles driven by colored noise can be approximately mapped onto a system that obeys detailed balance. The effective interactions which can be derived for such a system allow to describe the structure and phase behavior of the active fluid by means of an effective free energy. In this paper we explain why the related thermodynamic results for pressure and interfacial tension do not represent the results one would measure mechanically. We derive a dynamical density fu...

We investigate the effect of self-propulsion on a mean-field order-disorder transition. Starting from a $\varphi^4$ scalar field theory subject to an exponentially correlated noise, we exploit the Unified Colored Noise Approximation to map the non-equilibrium active dynamics onto an effective equilibrium one. This allows us to follow the evolution of the second-order critical point as a function of the noise parameters: the correlation time $\tau$ and the noise strength $D$. ...

We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal disorder gives rise to a distinct type of critical points at which the effective noise amplitude diverges on long time scales. This leads to enormous density fluctuations characterized by an infinitely broad probability distribution at cri...