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arXiv · 1207.5810

Ordering dynamics of the multi-state voter model

Michele Starnini·Andrea Baronchelli·Romualdo Pastor-Satorras
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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.

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Michele Starnini, Andrea Baronchelli, Romualdo Pastor-Satorras. 2012-10-30. Ordering dynamics of the multi-state voter model. https://doi.org/10.1088/1742-5468%2F2012%2F10%2Fp10027

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