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In this study, we performed Monte Carlo simulations of the $q=3,4$-Pottsmodel on quasiperiodic decagonal lattices (QDL) to assess the critical behaviorof these systems. Using the single histogram technique in conjunction with thefinite-size scaling analysis, we estimate the infinite lattice criticaltemperatures and the leading critical exponents for $q=3$ and $q=4$ states. Ourestimates for the critical exponents on QDL are in good agreement with theexact 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 universalityclass as those on 2D periodic lattices.

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