2003/11/30 by Wellington G. Dantas, Armando Ticona, Jurgen F. Stilck
Physics and Astronomy · #cond-mat.stat-mech
published as Braz. J. Phys, 35, 536 (2005) · 9 pages and 17 figures
arxiv created 2005/06/11 · arxiv updated 2009/12/01
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.