MONTE-CARLO STUDY OF THE XY-MODEL ON PENROSE LATTICES

We have carried out a Monte Carte study of the nearest-neighbour ferro magnetic XY-model on the two-dimensional (2D) Penrose lattice and on p eriodically stacked (three-dimensional) 2D Penrose lattices. For the 2 D case we have examined the magnetization, specific heat, linear susce ptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all of these qu antities points to a Kosterlitz-Thouless transition occurring in the t emperature range T-c = (1.0-1.05)J/K-B, with critical exponents that a re consistent with those obtained for crystalline (e.g., square) latti ces. For the 3D stacking of the 2D Penrose lattices, examination of th e magnetization, specific heat and linear susceptibility reveals a con ventional second-order phase transition. Through cumulant analysis and finite-size scaling we obtain a critical temperature T-c = (2.292 +/- 0.003)J and critical exponents alpha' = 0.03 +/- 0.03, beta = 0.30 +/ - 0.01 and gamma = 1.31 +/- 0.02, in agreement with previous studies o f the XY-model on the 3D cubic lattice.