Contact processes with competitive dynamics in bipartite lattices: Effects of distinct interactions

Abstract

The two-dimensional contact process (CP) with a competitive dynamics proposed by Martins {\it et al.} [Phys. Rev. E {\bf 84}, 011125(2011)] leads to the appearance of an unusual active asymmetric phase, in which the system sublattices are unequally populated. It differs from the usual CP only by the fact that particles also interact with their next-nearest neighbor sites via a distinct strength creation rate and for the inclusion of an inhibition effect, proportional to the local density. Aimed at investigating the robustness of such asymmetric phase, in this paper we study the influence of distinct interactions for two bidimensional CPs. In the first model, the interaction between first neighbors requires a minimal neighborhood of adjacent particles for creating new offspring, whereas second neighbors interact as usual (e.g. at least one neighboring particle is required). The second model takes the opposite situation, in which the restrictive dynamics is in the interaction between next-nearest neighbors sites. Both models are investigated under mean field theory (MFT) and Monte Carlo simulations. In similarity with results by Martins {\it et. al.}, the inclusion of distinct sublattice interactions maintain the occurrence of an asymmetric active phase and reentrant transition lines. In contrast, remarkable differences are presented, such as discontinuous phase transitions (even between the active phases), the appearance of tricritical points and the stabilization of active phases under larger values of control parameters. Finally, we have shown that the critical behaviors are not altered due to the change of interactions, in which the absorbing transitions belong to the directed percolation (DP) universality class, whereas second-order active phase transitions belong to the Ising universality class.