Absence of ferromagnetism in Ising model on directed Barabasi-Albert network

TL;DR

This study uses Monte Carlo simulations to investigate whether spontaneous magnetization exists in the Ising model on directed Barabasi-Albert networks, finding that magnetization decays over time and diverges at zero temperature.

Contribution

It provides the first large-scale simulation evidence that spontaneous magnetization does not persist in this network model, extending previous findings.

Findings

Magnetization decays after a characteristic time tau(T).

Tau(T) diverges at zero temperature, possibly following a modified Arrhenius or power law.

No evidence of stable ferromagnetism in the studied network model.

Abstract

With up to 7 million spins, the existence of spontaneous magnetization of Ising spins on directed Barabasi-Albert networks is investigated by Monte Carlo simulations. We confirm our earlier result that the magnetization for different temperatures T decays after a characteristic time tau(T), which we extrapolate to diverge at zero temperature by a modified Arrhenius law,or perhaps a power law.