title: Majority rule dynamics in finite dimensions.
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.
authors.affiliation: Center for BioDynamics, Center for Polymer Studies, and Department of Physics, Boston University, Boston, MA 02215, USA. patrick@bu.edu
authors.forename: P
authors.initials: P
authors.lastname: Chen
authors.forename: S
authors.initials: S
authors.lastname: Redner