Discontinuous phase transition in an annealed multi-state majority-vote model

Abstract

In this paper, we generalize the original majority-vote (MV) model with noise from two states to arbitrary $q$ states, where $q$ is an integer no less than two. The main emphasis is paid to the comparison on the nature of phase transitions between the two-state MV (MV2) model and the three-state MV (MV3) model. By extensive Monte Carlo simulation and mean-field analysis, we find that the MV3 model undergoes a discontinuous order-disorder phase transition, in contrast to a continuous phase transition in the MV2 model. A central feature of such a discontinuous transition is a strong hysteresis behavior as noise intensity goes forward and backward. Within the hysteresis region, the disordered phase and ordered phase are coexisting.

12 pages, 6 figures

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• Statistical physics of social dynamics
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• Phase transitions in a multistate majority-vote model on complex networks
• Switching from a continuous to discontinuous phase transition under the quenched disorder
• Finite-size effects on the convergence time in continuous-opinion dynamics
• Phase diagram in a one-dimensional civil disorder model
• When heterogeneity drives hysteresis: Anticonformity in the multistate $q$-voter model on networks