Majority versus minority dynamics: Phase transition in an interacting two-state spin system

M. Mobilia and S. Redner
Phys. Rev. E 68, 046106 – Published 9 October 2003
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Abstract

We introduce a simple model of opinion dynamics in which binary-state agents evolve due to the influence of agents in a local neighborhood. In a single update step, a fixed-size group is defined and all agents in the group adopt the state of the local majority with probability p or that of the local minority with probability 1p. For group size G=3, there is a phase transition at pc=2/3 in all spatial dimensions. For p>pc, the global majority quickly predominates, while for p<pc, the system is driven to a mixed state in which the densities of agents in each state are equal. For p=pc, the average magnetization (the difference in the density of agents in the two states) is conserved and the system obeys classical voter model dynamics. In one dimension and within a Kirkwood decoupling scheme, the final magnetization in a finite-length system has a nontrivial dependence on the initial magnetization for all ppc, in agreement with numerical results. At pc, the exact two-spin correlation functions decay algebraically toward the value 1 and the system coarsens as in the classical voter model.

  • Received 4 June 2003

DOI:https://doi.org/10.1103/PhysRevE.68.046106

©2003 American Physical Society

Authors & Affiliations

M. Mobilia and S. Redner*

  • Center for BioDynamics, Center for Polymer Studies & Department of Physics, Boston University, Boston, Massachusetts 02215, USA

  • *Electronic address: mmobilia,redner@bu.edu

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Vol. 68, Iss. 4 — October 2003

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