Critical Behavior of the q = 3, 4-Potts model on Quasiperiodic Decagonal Lattices

Abstract: In this study, we performed Monte Carlo simulations of the $q=3,4$-Potts model on quasiperiodic decagonal lattices (QDL) to assess the critical behavior of these systems. Using the single histogram technique in conjunction with the finite-size scaling analysis, we estimate the infinite lattice critical temperatures and the leading critical exponents for $q=3$ and $q=4$ states. Our estimates for the critical exponents on QDL are in good agreement with the exact values on 2D periodic lattices, supporting the claim that both the $q=3$ and $q=4$ Potts model on quasiperiodic lattices belong to the same universality class as those on 2D periodic lattices.