Disorder induced phase transition in an opinion dynamics model: results in 2 and 3 dimensions

TL;DR

This paper investigates a continuous opinion dynamics model with mixed interactions, revealing a phase transition between consensus and disorder in 2D and 3D, with critical behavior matching the Ising universality class.

Contribution

The study extends previous mean field analysis by numerically exploring the model in two and three dimensions, estimating critical points and exponents.

Findings

Identified continuous phase transition between consensus and disorder.

Estimated critical points and exponents in 2D and 3D.

Found universality class matches the Ising model.

Abstract

We study a model of continuous opinion dynamics with both positive and negative mutual interaction. The model shows a continuous phase transition between a phase with consensus (order) and a phase having no consensus (disorder). The mean field version of the model was already studied. Using extensive numerical simulations, we study the same model in $2$ and $3$ dimensions. The critical points of the phase transitions for various cases and the associated critical exponents have been estimated. The universality class of the phase transitions in the model is found to be same as Ising model in the respective dimensions.