Critical behavior of the two- and three-dimensional contact replication processes

Abstract

The two- and three-dimensional contact replication processes (CRP) for monoclonal reproduction were analyzed through intensive Monte Carlo simulations. In these models, the occupation rates are equally divided among the empty nearest neighbor sites of an occupied site. As the one-dimensional case, the two-dimensional version of the model belongs to the directed percolation universality class and the critical rate defining the absorbing state transition is lambdac = 1.083 20(7). However, the critical exponents of the three-dimensional CRP are those of the four-dimensional original contact process and, consequently, the data suggest that the CRP model has a distinct upper critical dimension dc = 3.