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 …