Abstract
We investigate the critical properties of a one-dimensional stochastic lattice model with n (permutation symmetric) absorbing states. We analyze the cases with by means of the nonhermitian density-matrix renormalization group. For and we find that the model is, respectively, in the directed percolation and parity conserving universality class, consistent with previous studies. For and 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 limit, the dynamics of the model can be mapped onto that of a zero temperature n-state Potts model. On the basis of our numerical and analytical results, we conjecture that the model is in the same universality class for all with exponents and β=1. These exponents coincide with those of the multispecies (bosonic) branching annihilating random walks. For we also show that, upon breaking the symmetry to a lower one one gets a transition either in the directed percolation, or in the parity conserving class, depending on the choice of parameters.
- Received 24 April 2001
DOI:https://doi.org/10.1103/PhysRevE.64.036124
©2001 American Physical Society