Monte Carlo simulations of the Ising and the Sznajd model on growing Barabasi - Albert networks

TL;DR

This paper uses Monte Carlo simulations to study the behavior of the Ising and Sznajd models on growing Barabasi-Albert networks, revealing ferromagnetic properties, hysteresis, and opinion dynamics depending on growth rate and opinion number.

Contribution

It demonstrates how dynamic network growth influences phase transitions and opinion consensus in classical models, extending static network results to evolving networks.

Findings

Ising model shows ferromagnetic behavior on growing networks

Sznajd model exhibits hysteresis and history-dependent consensus

Opinion dynamics depend on network growth rate and number of opinions

Abstract

The Ising model shows on growing Barabasi - Albert networks the same ferromagnetic behavior as on static Barabasi - Albert networks. Sznajd models on growing Barabasi - Albert networks show an hysteresis like behavior. Nearly a full consensus builds up and the winning opinion depends on history. On slow growing Barabasi - Albert networks a full consensus builds up. At five opinions in the Sznajd model with limited persuasion on growing Barabasi - Albert networks, all odd opinions win and all even opinions loose supporters.