Disorder induced phase transition in kinetic models of opinion dynamics

TL;DR

This paper introduces a model of opinion dynamics with positive and negative interactions, revealing a universal phase transition at a critical negative interaction fraction, with implications for understanding social consensus formation.

Contribution

It presents a novel continuous opinion model incorporating both positive and negative interactions and analyzes its phase transition behavior through exact calculations and simulations.

Findings

Existence of a universal continuous phase transition at a critical negative interaction fraction p_c.

The transition resembles a ferromagnetic-paramagnetic phase transition with similar critical exponents.

Distinct features relevant to social systems are identified in the model.

Abstract

We propose a model of continuous opinion dynamics, where mutual interactions can be both positive and negative. Different types of distributions for the interactions, all characterized by a single parameter $p$ denoting the fraction of negative interactions, are considered. Results from exact calculation of a discrete version and numerical simulations of the continuous version of the model indicate the existence of a universal continuous phase transition at p=p_c below which a consensus is reached. Although the order-disorder transition is analogous to a ferromagnetic-paramagnetic phase transition with comparable critical exponents, the model is characterized by some distinctive features relevant to a social system.