DYNAMICAL POTENTIALS FOR NON-EQUILIBRIUM STATIONARY STATES DRIVEN BY MULTIPLICATIVE STOCHASTIC PROCESSES
Daniel G. Barci1; Zochil González Arenas1; Miguel V. Moreno1
1 University of the State of Rio de Janeiro
Resumo
We present a study on out-of-equilibrium phase transitions induced by multiplicative noise. Based on a re- cently developed path integral formalism, we built up a "dy- namical potential' written in terms of an order parameter ca- pable to describe non-equilibrium phase transitions. As an example, we applied our formalism to a particularly simple model which captures the physics of non-equilibrium phase transition. The model is defined by a set of stochastic vari- ables arranged in a hyper-cubic lattice satisfying a system of interacting Langevin equations with multiplicative noise. We computed a potential for the non-equilibrium stationary state in the saddle-point plus Gaussian fluctuations approximation. We discovered a phase transition with reentrant behavior for sufficiently strong lattice coupling. We computed the phase diagram for different dimensions and for different values of the stochastic prescription used to define the multiplicative stochastic process. We found that, at the level of this approx- imation, the phase transition is continuous and we computed critical exponents. Even thought, the concept of universal- ity is not completely developed in out-of-equilibrium transi- tions, the computed exponents are in the universality class of the dynamical Ising model.
Palavras-chave: Stochastic processes; multiplicative noise; non equilibrium stationary states; phase transitions