A general creation-annihilation model with absorbing states

TL;DR

This paper introduces a one-dimensional stochastic model with creation and annihilation processes, analyzing its phase transitions between active and absorbing states through theoretical and numerical methods.

Contribution

It presents a new creation-annihilation model with an exact solution and detailed phase diagram, connecting contact process and voter model universality classes.

Findings

Identified a continuous transition line between active and absorbing phases.

Located the transition point where the model shifts from continuous to discontinuous.

Estimated critical exponents and studied crossover between universality classes.

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 to 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.