English

Ordering dynamics of the multi-state voter model

Statistical Mechanics 2015-06-05 v2 Social and Information Networks Physics and Society

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.

Keywords

Cite

@article{arxiv.1207.5810,
  title  = {Ordering dynamics of the multi-state voter model},
  author = {Michele Starnini and Andrea Baronchelli and Romualdo Pastor-Satorras},
  journal= {arXiv preprint arXiv:1207.5810},
  year   = {2015}
}
R2 v1 2026-06-21T21:40:53.436Z