  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.
