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

TL;DR

This paper investigates the generalized voter class in two-dimensional spin models, revealing non-universal features such as nontrivial exit probabilities and anomalous consensus times due to nonconservation of magnetization.

Contribution

It demonstrates that different models within the generalized voter class exhibit distinct ordering dynamics, contrasting with the linear voter model, especially under unbalanced initial conditions.

Findings

Exit probability has a nontrivial shape in nonlinear voter models.

Magnetization is strongly nonconserved during early dynamics.

Consensus time shows anomalous, nonuniversal dependence on initial conditions.

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 $x$.