Order-disorder transition in a model with two symmetric absorbing states

Critical phenomena in the presence of symmetric absorbing states: A microscopic spin model with tunable parameters

The Langevin description of systems with two symmetric absorbing states yields a phase diagram with three different phases (disordered and active, ordered and active, absorbing) separated by critical lines belonging to three different universality classes (generalized voter, Ising, and directed percolation). In this paper we present a microscopic spin model with two symmetric absorbing states that has the property that the model parameters can be varied in a continuous way. Our results, obtained through extensive numerical simulations, indicate that all features of the Langevin description are encountered for our two-dimensional microscopic spin model. Thus the Ising and direction percolation lines merge into a generalized voter critical line at a point in parameter space that is not identical to the classical voter model. A vast range of different quantities are used to determine the universality classes of the order-disorder and absorbing phase transitions. The investigation of time-dependent quantities at a critical point belonging to the generalized voter universality class reveals a more complicated picture than previously discussed in the literature.

Order-parameter critical exponent of absorbing phase transitions in one-dimensional systems with two symmetric absorbing states

Via extensive Monte Carlo simulations along with systematic analyses of corrections to scaling, we estimate the order parameter critical exponent β of absorbing phase transitions in systems with two symmetric absorbing states. The value of β was conjectured to be 13/14≈0.93 and Monte Carlo simulation studies in the literature have repeatedly reproduced values consistent with the conjecture. In this paper, we systematically estimate β by analyzing the effective exponent after finding how strong corrections to scaling are. We show that the widely accepted numerical value of β is not correct. Rather, we obtain β=1.020(5) from different models with two symmetric absorbing states.