Magnetic properties of static and phason-disordered Penrose lattices

The Ising model of Penrose lattices is studied. The exponents as well as the critical amplitudes are calculated for a series of rational (periodic) approximants, with and without thermal phason fluctuations. In both cases, the determined exponents are very close to what is known for the Ising model of the square lattice. The critical amplitudes display systematic variations between the different approximants but remain finite and non-zero, leading to the conclusion that the Ising model of Penrose lattices belongs to the same universality class as the Ising model of square lattices, even when phason fluctuations are present. This result is consistent with the Fisher renormalization of the exponents in the presence of annealed disorder.