Noise and disorder: phase transitions and universality in a model of opinion formation

TL;DR

This paper investigates a 3-state opinion formation model incorporating independence and conviction, revealing universal critical behavior akin to the mean-field Ising model and showing how certain distributions can eliminate phase transitions.

Contribution

It introduces a novel 3-state opinion model with two mechanisms, analyzing their effects on phase transitions and universality classes.

Findings

Critical exponents are universal across the order-disorder transition.

The model exhibits the same universality class as the mean-field Ising model.

Certain conviction distributions can suppress phase transitions.

Abstract

In this work we study a 3-state opinion formation model considering two distinct mechanisms, namely independence and conviction. Independence is introduced in the model as a noise, by means of a probability of occurrence $q$. On the other hand, conviction acts as a disorder in the system, and it is introduced by two discrete probability distributions. We analyze the effects of such two mechanisms on the phase transitions of the model, and we found that the critical exponents are universal over the order-disorder frontier, presenting the same universality class of the mean-field Ising model. In addition, for one of the probability distributions the transition may be eliminated for a wide range of the parameters.