Explosive Phase Transition in a Majority-Vote Model with Inertia

TL;DR

This paper introduces an inertia component into the majority-vote model, leading to a sudden, explosive phase transition with hysteresis, contrasting the usual continuous transition, and provides both numerical and analytical insights.

Contribution

It presents a novel majority-vote model with inertia that causes a discontinuous phase transition, supported by numerical simulations and mean-field theoretical analysis.

Findings

Transition changes from continuous to explosive with inertia

Hysteresis behavior observed in the phase transition

Coexistence of phases within the hysteresis region

Abstract

We generalize the original majority-vote model by incorporating an inertia into the microscopic dynamics of the spin flipping, where the spin-flip probability of any individual depends not only on the states of its neighbors, but also on its own state. Surprisingly, the order-disorder phase transition is changed from a usual continuous type to a discontinuous or an explosive one when the inertia is above an appropriate level. A central feature of such an explosive transition is a strong hysteresis behavior as noise intensity goes forward and backward. Within the hysteresis region, a disordered phase and two symmetric ordered phases are coexisting and transition rates between these phases are numerically calculated by a rare-event sampling method. A mean-field theory is developed to analytically reveal the property of this phase transition.