Three-state Potts model on Non-local Directed Small-World Lattices

Abstract

In this paper, we study the effects of non-local directed Small-World (NLDSW) disorder in the three-state Potts model as a form to capture the essential features shared by real complex systems where non-locality effects play a important role in the behavior of these systems. Using Monte Carlo techniques and finite-size scaling analysis, we estimate the infinite lattice critical temperatures and the leading critical exponents in this model. In particular, we investigate the first- to second-order phase transition crossover when NLDSW links are inserted. A cluster-flip algorithm was used to reduce the critical slowing down effect in our simulations. We find that for a NLDSW disorder densities $p<p^{*}=0.05(4)$, the model exhibits a continuous phase transition falling into a new universality class, which continuously depends on $p$, while for $p^{*}\leqslant p \leqslant 1.0$, the model presents a weak first-order phase transition.