Ordering dynamics of the multi-state voter model

Abstract: The voter model is a paradigm of ordering dynamics. At each time step, a random node is selected and copies the state of one of its neighbors. Traditionally, this state has been considered as a binary variable. Here, we relax this assumption and address the case in which the number of states is a parameter that can assume any value, from 2 to \infty, in the thermodynamic limit. We derive mean-field analytical expressions for the exit probability and the consensus time for the case of an arbitrary number of states. We then perform a numerical study of the model in low dimensional lattices, comparing the case of multiple states with the usual binary voter model. Our work generalizes the well-known results for the voter model, and sheds light on the role of the so far almost neglected parameter accounting for the number of states.