Monte Carlo study of the XY-model on Penrose lattices

Abstract

We have carried out a Monte Carlo study of the nearest-neighbour ferromagnetic XY-model on the two-dimensional (2D) Penrose lattice and on periodically stacked (three-dimensional) 2D Penrose lattices. For the 2D case we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all of these quantities points to a Kosterlitz-Thouless transition occurring in the temperature range , with critical exponents that are consistent with those obtained for crystalline (e.g., square) lattices. For the 3D stacking of the 2D Penrose lattices, examination of the magnetization, specific heat and linear susceptibility reveals a conventional second-order phase transition. Through cumulant analysis and finite-size scaling we obtain a critical temperature and critical exponents and , in agreement with previous studies of the XY-model on the 3D cubic lattice.