A symbiotic two-species contact process
  We study a contact process (CP) with two species that interact in a symbiotic manner. In our model, each site of a lattice may be vacant or host individuals of species A and/or B; multiple occupancy by the same species is prohibited. Symbiosis is represented by a reduced death rate, mu < 1, for individuals at sites with both species present. Otherwise, the dynamics is that of the basic CP, with creation (at vacant neighbor sites) at rate lambda and death of (isolated) individuals at a rate of unity. Mean-field theory and Monte Carlo simulation show that the critical creation rate, lambda_c (mu), is a decreasing function of mu, even though a single-species population must go extinct for lambda < lambda_c(1), the critical point of the basic CP. Extensive simulations yield results for critical behavior that are compatible with the directed percolation (DP) universality class, but with unusually strong corrections to scaling. A field-theoretical argument supports the conclusion of DP critical behavior. We obtain similar results for a CP with creation at second-neighbor sites and enhanced survival at first neighbors, in the form of an annihilation rate that decreases with the number of occupied first neighbors. 
Marcelo Martins de Oliveira, Renato Vieira Dos Santos, and Ronald   Dickman
cond-mat.stat-mech