Phase transitions in a multistate majority-vote model on complex networks

TL;DR

This paper extends the majority-vote model to multiple states on complex networks, revealing that for three or more states the phase transition becomes discontinuous, with hysteresis and phase coexistence, differing from the original two-state model.

Contribution

The study introduces a generalized multistate majority-vote model on complex networks and analyzes its phase transition nature, showing a shift from second-order to first-order transitions for three or more states.

Findings

For p≥3, the phase transition is discontinuous (first-order).

Hysteresis and phase coexistence are observed near the transition.

The transition type depends on network degree heterogeneity for p≥3.

Abstract

We generalize the original majority-vote (MV) model from two states to arbitrary $p$ states and study the order-disorder phase transitions in such a $p$-state MV model on complex networks. By extensive Monte Carlo simulations and a mean-field theory, we show that for $p\geq3$ the order of phase transition is essentially different from a continuous second-order phase transition in the original two-state MV model. Instead, for $p\geq3$ the model displays a discontinuous first-order phase transition, which is manifested by the appearance of the hysteresis phenomenon near the phase transition. Within the hysteresis loop, the ordered phase and disordered phase are coexisting and rare flips between the two phases can be observed due to the finite-size fluctuation. Moreover, we investigate the type of phase transition under a slightly modified dynamics [Melo \emph{et al.} J. Stat. Mech. P11032 (2010)]. We find that the order of phase transition in the three-state MV model depends on the degree heterogeneity of networks. For $p\geq4$, both dynamics produce the first-order phase transitions.