Majority Rule Dynamics in Finite Dimensions

Details Majority Rule Dynamics in Finite Dimensions Majority Rule Dynamics in Finite Dimensions

2004-08-10

arxiv.org/abs/cond-mat/0408219v2

Phys. Rev. E 71, 036101 (2005)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 2-column revtex format, 11 figures. Version 2: minor changes in response to referee comments and typos corrected; fin

Scientific paper

10.1103/PhysRevE.71.036101

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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