Independence role in the generalized Sznajd model

TL;DR

This paper explores how independent agents influence the generalized Sznajd opinion model on different network structures, revealing that system behavior depends on paired agents and that the model aligns with Ising universality classes.

Contribution

It introduces a generalized Sznajd model with independent agents, analyzing its behavior on complete graphs and square lattices, and identifies its universality classes.

Findings

System state depends only on paired agents, not neighbor size.

Time to reach stationarity is inversely proportional to neighbor size.

Model on both networks belongs to the Ising universality class.

Abstract

The Sznajd model is one of sociophysics's well-known opinion dynamics models. Based on social validation, it has found application in diverse social systems and remains an intriguing subject of study, particularly in scenarios where interacting agents deviate from prevailing norms. This paper investigates the generalized Sznajd model, featuring independent agents on a complete graph and a two-dimensional square lattice. Agents in the network act independently with a probability $p$, signifying a change in their opinion or state without external influence. This model defines a paired agent size $r$, influencing a neighboring agent size $n$ to adopt their opinion. This study incorporates analytical and numerical approaches, especially on the complete graph. Our results show that the macroscopic state of the system remains unaffected by the neighbor size $n$ but is contingent solely on the number of paired agents $r$. Additionally, the time required to reach a stationary state is inversely proportional to the number of neighboring agents $n$. For the two-dimensional square lattice, two critical points $p = p_c$ emerge based on the configuration of agents. The results indicate that the universality class of the model on the complete graph aligns with the mean-field Ising universality class. Furthermore, the universality class of the model on the two-dimensional square lattice, featuring two distinct configurations, is identical and falls within the two-dimensional Ising universality class.