Universal and nonuniversal features of the generalized voter class for ordering dynamics in two dimensions

Abstract

By considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions [Dornic et al., Phys. Rev. Lett. 87, 045701 (2001)], we show that they behave differently from the linear voter model when the initial configuration is an unbalanced mixture of up and down spins. In particular, we show that for nonlinear voter models the exit probability (probability to end with all spins up when starting with an initial fraction x of them) assumes a nontrivial shape. This is the first time a nontrivial exit probability is observed in two-dimensional systems. The change is traced back to the strong nonconservation of the average magnetization during the early stages of dynamics. Also the time needed to reach the final consensus state T(N)(x) has an anomalous nonuniversal dependence on x.