Análise do comportamento crítico de modelos de não-equilíbrio na presença de voos de Lévy

Abstract

In the present in the present work we investigate continuous phase transitions of nonequilibrium in models with diffusion, branching and annihilation processes. Initially, we consider a parity conserving model of branching and annihilating random walkers with long-range diffusion. We obtained the set of critical exponents associated to the growth in the number particles and its fluctuations, as well as the second- order moment ratio. Diffusion and branching processes are controlled by a diffusion probability p and the flight distance follows a Lévy distribution with exponent α. Three regimes were identified, in function of the Lévy exponent α: for α ≤ 5/2 infinitesimal branching is relevant and leads to an explosive growth of the particle number (a phase transition takes place for α > 5/2); short-range power-law scaling occurs for α > 7/2; in the intermediate regime (3/2 < α < 7/2), continuously varying exponents. In another contribution, we study the dynamics of the branching and annihilating process with long-range interactions. Static particles generate an offspring and annihilate upon contact. The branching distance is supposed to follow a Lévy-like power law distribution. We analyze the long term behavior of the mean particles number and its fluctuations as a function of the parameter α that controls the range of the branching process. We show that the dynamic exponente associated with the particle number fluctuations varies continuously for α < 4, while the particle number exponent only changes for α < 3. We report extreme value distributions, Frechet ( for α = 3) e Gumbell (for 2 < α < 3). For α > 3, Gaussian distributions were observed. We use Monte Carlo simulations.