Two competitive contact processes with local interactions

Abstract

We present a simple lattice model that consists of two competitive contact processes with local interactions on a one-dimensional lattice. The sites of the lattice can be empty or occupied by particles of type A or type B. The time evolution of the densities is governed by a master equation, whose transition among the states depends essentially on the spreading and annihilation rates of both particles. This is a competitive model where the stationary states are determined as a function of the spreading and annihilation rates. We employ mean-field approximations, at the level of one and two sites, and we obtain a phase diagram that shows four well distinguished phases, including a mixed one in which both particles coexist. Monte Carlo simulations show that this mixed phase no longer exists in the limit of large one-dimensional lattices. However, simulations of the model in two dimensions show that the mixed phase does not disappear as in the one-dimensional case. We also calculate some static critical exponents of the one-dimensional version of the model and we have shown that they belong to the directed percolation universality class.

Continuously varying critical order-parameter fluctuations in a parity conserving absorbing-state transition with long-range diffusion

“…In order to precisely locate the transition between the active and absorbing states, we explore the hypothesis of scale invariance of the moment ratio m( p ) at the critical point. According to this scaling hypothesis, curves of the moment ratio obtained from simulations on distinct chain sizes are expected to cross at a single point which identifies both the critical probability p c and the critical moment ratio m c [30][31][32][33][34][35][36]. In and four distinct chain sizes.…”

“…Field theoretical and simulation results have unveiled that the critical exponents vary continuously with α for both cases of conserving and non-conserving parity of the number of particles [20,28,29]. To probe the fluctuations of the order parameter has been considered one relevant action aiming to fully characterize the critical behavior of non-equilibrium phase transitions [30][31][32][33][34][35][36]. It has been well established that the relative fluctuation of the order parameter becomes scale invariant at the transition with its critical value being a universal quantity.…”

Phase diagram of the symbiotic two-species contact process

“…Interacting, spatially extended, multi-species processes are a subject of recent interest [3][4][5][6][7][8][9]. In particular, multispecies (or multitype) contact processes have been used to model systems with neutral community structure, and have proven useful in understanding abundance distributions and species-area relationships [10,11].…”