Potts model with q=3 and 4 states on directed Small-World network
  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. 
P. R. O. da Silva, F.W.S. Lima, and R. N. Costa Filho
cond-mat.stat-mech cond-mat.dis-nn