Noise-induced absorbing phase transition in a model of opinion formation

TL;DR

This paper investigates a three-state opinion model with noise and disorder, revealing multiple phase transitions including Ising and directed percolation universality classes through analytical and numerical methods.

Contribution

It introduces an analytical framework for a 3-state opinion model with noise and disorder, identifying distinct phase transitions and their universality classes.

Findings

Identified ferro-paramagnetic transition in the Ising universality class.

Discovered para-absorbing and ferro-absorbing transitions in the directed percolation class.

Derived analytical expressions for order parameters and stationary opinion fractions.

Abstract

In this work we study a 3-state ($+1$, $-1$, $0$) opinion model in the presence of noise and disorder. We consider pairwise competitive interactions, with a fraction $p$ of those interactions being negative (disorder). Moreover, there is a noise $q$ that represents the probability of an individual spontaneously change his opinion to the neutral state. Our aim is to study how the increase/decrease of the fraction of neutral agents affects the critical behavior of the system and the evolution of opinions. We derive analytical expressions for the order parameter of the model, as well as for the stationary fraction of each opinion, and we show that there are distinct phase transitions. One is the usual ferro-paramagnetic transition, that is in the Ising universality class. In addition, there are para-absorbing and ferro-absorbing transitions, presenting the directed percolation universality class. Our results are complemented by numerical simulations.