Potts model with q=3 and 4 states on directed Small-World network

TL;DR

This study uses Monte Carlo simulations to analyze phase transitions in q=3 and 4 state Potts models on directed Small-World networks, revealing different critical behaviors compared to regular lattices.

Contribution

It investigates how directed Small-World network topology affects phase transition order in Potts models with q=3 and 4 states.

Findings

q=3 exhibits both first- and second-order transitions depending on p

q=4 shows only first-order transitions regardless of p

Critical behavior differs from that on regular square lattices

Abstract

Monte Carlo simulations are performed to study the two-dimensional Potts models with q=3 and 4 states on directed Small-World network. The disordered system is simulated applying the Heat bath Monte Carlo update algorithm. A first-order and second-order phase transition is found for q=3 depending on the rewiring probability $p$, but for q=4 the system presents only a first-order phase transition for any value $p$ . This critical behavior is different from the Potts model on a square lattice, where the second-order phase transition is present for $q\le4$ and a first-order phase transition is present for q>4.