Boundary effects in a three-state modified voter model for languages

TL;DR

This paper investigates how boundary conditions and noise influence opinion dynamics in a modified three-state voter model, revealing that boundaries can determine the dominant choice and noise stabilizes diverse opinions.

Contribution

It introduces a modified three-state voter model with boundary effects and noise, highlighting their roles in opinion stability and dominance, supported by Monte Carlo simulations.

Findings

Boundaries can lead to the dominance of a single choice.

Noise stabilizes the coexistence of all three opinions.

Removing fixed boundaries can change the winning opinion.

Abstract

The standard three-state voter model is enlarged by including the outside pressure favouring one of the three choices and by adding some biased internal random noise. The Monte Carlo simulations are motivated by states with the population divided into three groups of various affinities to each other. We show the crucial influence of the boundaries for moderate lattice sizes like 500 x 500. By removing the fixed boundary at one side, we demonstrate that this can lead to the victory of one single choice. Noise in contrast stabilizes the choices of all three populations. In addition, we compute the persistence probability, i.e., the number of sites who have never changed their opinion during the simulation, and we consider the case of "rigid-minded" decision makers.