A general creation-annihilation model with absorbing states

Abstract

A one dimensional non-equilibrium stochastic model is proposed where each site of the lattice is occupied by a particle, which may be of type A or B. The time evolution of the model occurs through three processes: autocatalytic generation of A and B particles and spontaneous conversion A → B. The two-parameter phase diagram of the model is obtained in one-and two-site mean field approximations, as well as through numerical simulations and exact solution of finite systems extrapolated to the thermodynamic limit. A continuous line of transitions between an active and an absorbing phase is found. This critical line starts at a point where the model is equivalent to the contact process and ends at a point which corresponds to the voter model, where two absorbing states coexist. Thus, the critical line ends at a point where the transition is discontinuous. Estimates of critical exponents are obtained through the simulations and finite-size-scaling extrapolations, and the crossover between universality classes as the voter model transition is approached is studied.

A supercritical series analysis for the generalized contact process with diffusion

“…The lowest order of mean-field cluster approximation in which the effect of diffusion is present in the results is the two-site approximation. Without going into the details of this approximation, since the calculations are similar to the ones performed recently in the model without diffusion [9], in the two-site level cluster approximation the critical line is given by:…”

“…Recently, a generalization of the CP was studied using mean-field approximations and simulations [9], as well as series expansions [10]. In this model, an additional process is included besides the autocatalytic creation and the spontaneous annihilation of particles: the autocatalytic creation of holes, that is, an occupied site may become empty by two processes: either spontaneously or with a rate which is proportional to the number of empty first-neighbour sites.…”