Frustrated classical XY spin systems in the two-dimensional Penrose tiling

Abstract

Magnetic ground states of frustrated classical XY spin systems in a finite two-dimensional Penrose tiling are determined by Monte Carlo simulations using the simulated annealing method. The interactions are limited to the third neighbours ( J 1, J 2, J 3) and the next nearest neighbour interaction is assumed to be antiferromagnetic. If frustration is low, the ground state is antiferromagnetic. If J 1 or J 3 is positive, increasing the absolute value of the negative exchange integral ( J 3 or J 1, respectively) which increases the local frustration does not break up the magnetic order but only broadens the two peaks of the spin angular distribution. There is evidence for a Kosterlitz-Thouless transition, as in periodic systems, in the thermal variation of the specific heat. This transition temperature is found to be independent of the nearest neighbour interaction, J 1, but varies linearly with the third neighbour one, J 3.