Ising model S=1, 3/2 and 2 on directed networks

TL;DR

This study investigates the phase transition behavior of the Ising model with spins S=1, 3/2, and 2 on directed Small-World and Barabasi-Albert networks using Monte Carlo simulations, revealing different transition types depending on network parameters.

Contribution

It provides the first detailed analysis of how spin magnitude and network topology influence phase transitions in directed networks.

Findings

Second-order phase transition at p=0.2 on Small-World networks.

First-order phase transition at p=0.8 on Small-World networks.

No phase transition observed on directed Barabasi-Albert networks.

Abstract

On directed} Barabasi-Albert and Small-World networks the Ising model with spin S=1, 3/2 and 2 is now studied through Monte Carlo simulations. In this model, the order-disorder phase transition of the order parameter is well defined on Small-World networks for Ising model with spin S=1. We calculate the value of the critical temperature T_c for several values of rewiring probability p of the directed Small-World network. This model on directed Small-World networks we obtained a second-order phase transition for p=0.2 and first-order phase transition for p=0.8. The critical exponentes beta/nu, gamma/nu and 1/\nu were calculated for p=0.2. On directed Barabasi-Albert we show that no there is phase transition for Ising model with spin S=1, 3/2 and 2.