Three-state Potts model on non-local directed small-world lattices

• Published in: Physica A Vol. 484; pp. 488 - 498
• Main Authors: Ferraz, Carlos Handrey Araujo, Lima, José Luiz Sousa
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.10.2017
• Subjects: Critical exponents; Disorder density; Monte Carlo method; Potts model; Small-World lattices; Monte Carlo method; Potts model; Small-World lattices; Disorder density; Critical exponents
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2017.05.016

In this paper, we study the non-local directed Small-World (NLDSW) disorder effects 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 the value of p, while for p∗⩽p⩽1.0, the model presents a weak first-order phase transition. •q=3 Potts model on NLDSW lattices has a first-order phase transition for p>p∗=0.05.•q=3 Potts model on NLDSW lattices is a different universality class for 0.01≤p≤p∗.•We estimate the critical temperatures of the q=3 Potts model for 0.01≤p≤p∗.