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Majority Rule Dynamics in Finite Dimensions

P. Chen·S. Redner
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Abstract

We investigate the long-time behavior of a majority rule opinion dynamics model in finite spatial dimensions. Each site of the system is endowed with a two-state spin variable that evolves by majority rule. In a single update event, a group of spins with a fixed (odd) size is specified and all members of the group adopt the local majority state. Repeated application of this update step leads to a coarsening mosaic of spin domains and ultimate consensus in a finite system. The approach to consensus is governed by two disparate time scales, with the longer time scale arising from realizations in which spins organize into coherent single-opinion bands. The consequences of this geometrical organization on the long-time kinetics are explored.

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BibTeXRIS

P. Chen, S. Redner. 2004-12-16. Majority Rule Dynamics in Finite Dimensions. https://doi.org/10.1103/physreve.71.036101

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