Unusual ferromagnetism in Ising and Potts model on semi-directed Barab\'asi-Albert networks

TL;DR

This study investigates spontaneous magnetization in Ising and Potts models on semi-directed Barabási-Albert networks, revealing a temperature-dependent decay of magnetization with a divergence at a critical temperature that grows logarithmically with network size.

Contribution

It demonstrates the existence of a finite-temperature phase transition in these models on semi-directed networks, characterized by a divergence of the critical temperature with network size.

Findings

Magnetization decays over time at different temperatures.

Critical temperature increases logarithmically with network size.

Divergence of critical temperature follows Vogel-Fulcher law.

Abstract

We check the existence of a spontaneous magnetisation of Ising and Potts spins on semi-directed Barabasi-Albert networks by Monte Carlo simulations. We verified that the magnetisation for different temperatures $T$ decays after a characteristic time $\tau(T)$, which we extrapolate to diverge at positive temperatures $T_c(N)$ by a Vogel-Fulcher law, with $T_c(N)$ increasing logarithmically with network size $N$.