2001/06/06 by Jef Hooyberghs, Enrico Carlon, Carlo Vanderzande · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.64.036124
published as Phys. Rev. E 62, 036124 (2001) · 10 pages, RevTeX, and 10 PostScript figures included
arxiv created 2001/06/06 · openalex publication_date 2001/08/30 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We investigate the critical properties of a one-dimensional stochastic lattice model with n (permutation symmetric) absorbing states. We analyze the cases with n</=4 by means of the nonhermitian density-matrix renormalization group. For n=1 and n=2 we find that the model is, respectively, 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 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 n>/=3 with exponents z=nu( ||)/nu( perpendicular)=2, nu( perpendicular)=1, and beta=1. These exponents coincide with those of the multispecies (bosonic) branching annihilating random walks. For n=3 we also show that, upon breaking the symmetry to a lower one (Z2), one gets a transition either in the directed percolation, or in the parity conserving class, depending on the choice of parameters.