# Majority Rule Dynamics in Finite Dimensions

Source: [Majority Rule Dynamics in Finite Dimensions](<https://www.sota2.com/research/paper/68fa268f2c2a3760193bb208>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T03:05:26.850Z

Authors: P. Chen, S. Redner

Published: 2004-08-10T19:07:46.000Z

## 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0408219>)

[PDF](<https://arxiv.org/pdf/cond-mat/0408219.pdf>)