Universal and non-universal features of the generalized voter class for ordering dynamics

Abstract

By considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions [I. Dornic, \textit{et al.} Phys. Rev. Lett. \textbf{87}, 045701 (2001)], we show that they behave differently from the linear voter model when the initial configuration is an unbalanced mixture 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. 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 $x$.

7 pages, 7 figures

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• First-passage distributions for the one-dimensional Fokker-Planck equation
• A consensus opinion model based on the evolutionary game
• Opinion percolation in structured population
• Exit probability in inflow dynamics: nonuniversality induced by range, asymmetry and fluctuation
• Discontinuous phase transition in an open-ended Naming Game
• Kinetics of the one-dimensional voter model with long-range interactions
• Dynamics of Influence on Hierarchical Structures
• Critical phenomena in presence of symmetric absorbing states: a microscopic spin model with tunable parameters
• Dynamic critical properties of non-equilibrium Potts models with absorbing states