Mean-field-like behavior of the generalized voter-model-class kinetic Ising model

TL;DR

This paper investigates a kinetic Ising model with suppressed bulk noise, revealing mean-field-like phase transition behavior and analyzing the effects of absorbing states and finite size on the system's dynamics.

Contribution

It introduces a stationary state variant of the model and compares Fokker-Planck and mean field approaches to characterize the phase transition.

Findings

The system exhibits a mean-field-like phase transition.

Absorbing states cause dynamic slowing down.

Finite size effects influence the transition behavior.

Abstract

We analyze a kinetic Ising model with suppressed bulk noise which is a prominent representative of the generalized voter model phase transition. On the one hand we discuss the model in the context of social systems, and opinion formation in the presence of a tunable social temperature. On the other hand we characterize the abrupt phase transition. The system shows non-equilibrium dynamics in the presence of absorbing states. We slightly change the system to get a stationary state model variant exhibiting the same kind of phase transition. Using a Fokker-Planck description and comparing to mean field calculations, we investigate the phase transition, finite size effects and the effect of the absorbing states resulting in a dynamic slowing down.