Simulation of majority rule disturbed by power-law noise on directed and undirected Barabasi-Albert networks

TL;DR

This study uses Monte Carlo simulations to analyze how power-law noise affects the majority rule in Ising models on directed and undirected Barabasi-Albert networks, revealing different phase transition behaviors.

Contribution

It introduces a novel noise spectrum based on power-law distribution to model environmental influences in complex networks, contrasting with traditional lattice models.

Findings

Magnetization decays exponentially in directed networks.

Magnetization remains constant in undirected networks.

No order-disorder phase transition observed.

Abstract

On directed and undirected Barabasi-Albert networks the Ising model with spin S=1/2 in the presence of a kind of noise is now studied through Monte Carlo simulations. The noise spectrum P(n) follows a power law, where P(n) is the probability of flipping randomly select n spins at each time step. The noise spectrum P(n) is introduced to mimic the self-organized criticality as a model influence of a complex environment. In this model, different from the square lattice, the order-disorder phase transition of the order parameter is not observed. For directed Barabasi-Albert networks the magnetisation tends to zero exponentially and for undirected Barabasi-Albert networks, it remains constant.