Large deviation induced phase switch in an inertial majority-vote model

TL;DR

This paper investigates noise-induced phase switching in an inertial majority-vote model, revealing a first-order transition characterized by hysteresis and exponential switching times, validated through theoretical analysis and simulations.

Contribution

It introduces a theoretical framework using WKB approximation to analyze phase switches in an inertial majority-vote model, highlighting the role of noise and inertia in first-order transitions.

Findings

Hysteresis behavior indicates a first-order phase transition.

Switching times depend exponentially on system size and action.

Critical noise level $f_c$ marks phase coexistence point.

Abstract

We theoretically study noise-induced phase switch phenomena in an inertial majority-vote (IMV) model introduced in a recent paper [Phys. Rev. E 95, 042304 (2017)]. The IMV model generates a strong hysteresis behavior as the noise intensity $f$ goes forward and backward, a main characteristic of a first-order phase transition, in contrast to a second-order phase transition in the original MV model. Using the Wentzel-Kramers-Brillouin approximation for the master equation, we reduce the problem to finding the zero-energy trajectories in an effective Hamiltonian system, and the mean switching time depends exponentially on the associated action and the number of particles $N$. Within the hysteresis region, we find that the actions along the optimal forward switching path from ordered phase (OP) to disordered phase (DP) and its backward path, show distinct variation trends with $f$, and intersect at $f=f_c$ that determines the coexisting line of OP and DP. This results in a nonmonotonic dependence of the mean switching time between two symmetric OPs on $f$, with a minimum at $f_c$ for sufficiently large $N$. Finally, the theoretical results are validated by Monte Carlo simulations.