The impact of social noise on the majority rule model across various network topologies

TL;DR

This paper investigates how social noise, modeled as nonconformist behavior, influences phase transitions in the majority rule model across various network topologies, revealing a universal behavior akin to the Ising model.

Contribution

It introduces a comprehensive analysis of social noise effects on the majority rule model across multiple network types, establishing universality with the Ising model.

Findings

The model exhibits a continuous phase transition on all tested networks.

Critical exponents suggest the model belongs to the Ising universality class.

Social noise parameter p influences the order-disorder transition universally.

Abstract

We explore the impact of social noise, characterized by nonconformist behavior, on the phase transition within the framework of the majority rule model. The order-disorder transition can reflect the consensus-polarization state in a social context. This study covers various network topologies, including complete graphs, two-dimensional (2-D) square lattices, three-dimensional (3-D) square lattices, and heterogeneous or complex networks such as Watts-Strogatz (W-S), Barab\'asi-Albert (B-A), and Erd\H{o}s-R\'enyi (E-R) networks, as well as their combinations (multilayer network). Social behavior is represented by the parameter \( p \), which indicates the probability of agents exhibiting nonconformist behavior. Our results show that the model exhibits a continuous phase transition across all networks. Through finite-size scaling analysis and evaluation of critical exponents, our results suggest that the model falls into the same universality class as the Ising model.