The three-state majority-vote model with noise on Erdös–Rényi random graphs has
been studied. Using Monte Carlo simulations we obtain the phase diagram, along
with the critical exponents. Exact results for limiting cases are presented, and
shown to be in agreement with numerical values. We find that the critical noise
qc
is an increasing function of the mean connectivity
z
of the graph. The critical exponents , and are calculated for several values of the connectivity. We also study the globally connected
network, which corresponds to the mean-field limit . Our numerical results indicate that the correlation length scales with the number of
nodes in the graph, which is consistent with an effective dimensionality equal to unity.
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