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

TL;DR

This paper investigates the critical behavior of the q=3 and 4 Potts models on quasiperiodic decagonal lattices using Monte Carlo simulations, finite-size scaling, and histogram techniques, finding universality with 2D periodic lattices.

Contribution

It provides the first detailed estimate of critical temperatures and exponents for Potts models on quasiperiodic lattices, confirming universality class equivalence with periodic lattices.

Findings

Critical exponents match those of 2D periodic lattices.

Critical temperatures are accurately estimated.

Universality class is confirmed for quasiperiodic 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.