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Majority versus minority dynamics: Phase transition in an interacting two-state spin system
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 1-p. For group size G=3, there is a phase transition
at p_c=2/3 in all spatial dimensions. For p>p_c, the global majority quickly
predominates, while for p<p_c, the system is driven to a mixed state in which
the densities of agents in each state are equal. For p=p_c, 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 non-trivial dependence on the initial magnetization
for all p.ne.p_c, in agreement with numerical results. At p_c, the exact 2-spin
correlation functions decay algebraically toward the value 1 and the system
coarsens as in the classical voter model.Comment: 11 pages, 3 figures, revtex4 2-column format; minor revisions for
publication in PR