@bachelorsthesis{1994R,
  title={Monte-Carlo study of 2-d quasicrystals},
  author={Bill Reid},
  month={April},
  year={1994},
  abstract={Monte Carlo analysis was carried out on two dimensional systems in
two parts. In the first part, we cool a binary alloy, starting from a
random configuration and allow the particles to interact with a
Lennard-Jones type potential, whose parameters are chosen to reproduce a
Penrose-like lattice as the ground state of the binary system. We study
internal energy, density and specific heat for the system as a function of
temperature and compare the resulting ground state with a Penrose Lattice.
In the second part, we study the XY (planar spin) model on Penrose
lattices with free boundaries as well as periodic Penrose lattices (PPL).
Under conditions of cooling and heating, we examine internal energy,
specific heat, and susceptibility as a function of temperature, along with
angular displacement and order parameter &lt; M<sup>2</sup> &gt; as a function of
system size. Based on the behaviour of specific heat and susceptibility, we are
able to verify the Kosterlitz-Thouless theory of phase transition in the
2D XY model for Penrose lattices.},
  note={Supervised by S.K. Bose}
}