Critical behavior of the q=3,4q=3,4-Potts model on quasiperiodic decagonal lattices

•We estimate the critical exponents of the q=3,4q=3,4 Potts model on QDL.•We estimate the critical temperature of the q=3,4q=3,4 Potts model on QDL.•q=3,4q=3,4 Potts model on QDL and on periodic lattices are in the same universality class.

In this study, we performed Monte Carlo simulations of the q=3,4q=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=3q=3 and q=4q=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=3q=3 and q=4q=4 Potts model on quasiperiodic lattices belong to the same universality class as those on 2D periodic lattices.