Potts model with q states on directed Barabasi-Albert networks

TL;DR

This paper investigates the phase transition behavior of Potts models with q=3 and 8 states on directed Barabasi-Albert networks, revealing first-order transitions for both, contrasting with their behavior on 2D lattices.

Contribution

It presents the first Monte Carlo simulation study of q=3 and 8-state Potts models on directed Barabasi-Albert networks, showing first-order phase transitions for both q values.

Findings

First-order phase transitions observed for q=3 and 8.

Contrasts with second-order transition for q=3 on 2D lattices.

Network connectivity influences the order of phase transition.

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. However, on these networks the Ising model spin S=1 was seen to show a spontaneous magnetisation. In this model with spin S=1 a first-order phase transition for values of connectivity z=2 and z=7 is well defined. On these same networks the Potts model with q=3 and 8 states is now studied through Monte Carlo simulations. We have obtained also for q=3 and 8 states a first-order phase transition for values of connectivity z=2 and z=7 of the directed Barabasi-Albert network. Theses results are different from the results obtained for same model on two-dimensional lattices, where for q=3 the phase transition is of second order, while for q=8 the phase transition is first-order.