Generalized contact process with n absorbing states - art. no. 036124

We investigate the critical properties of a one-dimensional stochastic latt ice model with n (permutation symmetric) absorbing states. We analyze the c ases with n less than or equal to4 by means of the nonhermitian density-mat rix renormalization group. For n = 1 and n = 2 we find that the model is, r espectively, in the directed percolation and parity conserving universality class, consistent with previous studies. For n = 3 and n = 4, the model is in the active phase in the whole parameter space and the critical point is shifted to the limit of one infinite reaction rate. We show that in this l imit, the dynamics of the model can be mapped onto that of a zero temperatu re n-state Potts model. On the basis of our numerical and analytical result s, we conjecture that the model is in the same universality class for all n greater than or equal to 3 with exponents z = nu (parallel to)/nu (perpend icular to) = 2, nu (perpendicular to) = 1, and beta = 1. These exponents co incide with those of the multispecies (bosonic) branching annihilating rand om walks. For n = 3 we also show that, upon breaking the symmetry to a lowe r one (Z(2)), one gets a transition either in the directed percolation, or in the parity conserving class, depending on the choice of parameters.