Monte Carlo investigation of the eight-state Potts model on quasiperiodic tilings

Abstract

A Monte Carlo investigation of the eight-state Potts model on the two-dimensional (2D) quasiperiodic octagonal tiling with free boundary conditions is performed in order to determine the nature of a temperature-driven transition. It is shown that numerical data suffer from drastic free boundary effects that strongly disturb the probability distributions of the internal energy and, consequently, the scaling behavior of the specific heat. An alternative way consisting in analysing the core of the tilings is applied to pass over free boundary effects. This analysis combined with the Lee–Kosterlitz method allows one to evidence that the system undergoes a first-order transition as in 2D periodic lattices. The first-order type of scaling is observed for the maximum in the susceptibility of the core of the tilings but not for the maximum in the specific heat.