Monte-Carlo study of 2-d quasicrystals (bibtex)

by Bill Reid

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 < M^{2} > 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.

Reference:

Bill Reid, "Monte-Carlo study of 2-d quasicrystals", 1994.

Bibtex Entry:

@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 < M<sup>2</sup> > 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} }

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