Ordering dynamics of the multi-state voter model

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 address the case in which the number of states is a parameter that can assume any value, from 2 to ∞, in the thermodynamic limit. We derive mean-field analytical expressions for the exit probability, the consensus time, and the number of different states as a function of time for the case of an arbitrary number of states. We finally 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 sheds light on the role of the parameter accounting for the number of states. PACS numbers: 89.65.-s, 05.40.-a, 89.75.-k ar X iv :1 20 7. 58 10 v2 [ co nd -m at .s ta tm ec h] 3 0 O ct 2 01 2 Ordering dynamics of the multi-state voter model 2