Ising model spin S=1 on directed Barabasi-Albert networks

TL;DR

This study investigates the phase transition behavior of the S=1 Ising model on directed Barabasi-Albert networks, revealing a first-order transition at specific connectivities, contrasting with the S=1/2 case.

Contribution

It demonstrates the existence of a first-order phase transition in the S=1 Ising model on directed Barabasi-Albert networks, a novel finding compared to the S=1/2 case.

Findings

First-order phase transition observed at m=2 and m=7.

Contrasts with S=1/2 model which shows no spontaneous magnetization.

Magnetization decay behaviors differ between algorithms.

Abstract

On directed Barabasi-Albert networks with two and seven neighbours selected by each added site, the Ising model with spin S=1/2 was seen not to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation followed an Arrhenius law for Metropolis and Glauber algorithms, but for Wolff cluster flipping the magnetisation decayed exponentially with time. On these networks the Ising model spin S=1 is now studied through Monte Carlo simulations. However, in this model, the order-disorder phase transition is well defined in this system. We have obtained a first-order phase transition for values of connectivity m=2 and m=7 of the directed Barabasi-Albert network.