Ising model on Penrose lattices: Boundary conditions

The zero-field ferromagnetic Ising model is studied on three different geometries that all approach Penrose lattices. Two types of aperiodic boundary conditions are presented. By means of Monte Carlo simulation and finite-size scaling we determine with high accuracy the transition temperature, critical exponents η and ν, specific-heat critical amplitude, and several finite-size-scaling amplitudes, and we study the effects of different boundary conditions. In all cases, we find that η≊1/4 and ν≊1. Thus, we conclude that, despite its quasiperiodicity, the Ising model on the Penrose lattices belongs to the same universality class as Ising models on periodic lattices. We find that the aperiodic boundary conditions lead to finite-size-scaling functions different from those for periodic boundary conditions. However, the rates of convergence to the finite-size-scaling regime are comparable between different boundary conditions.