Numerical Simulations of the Ising Model on the Union Jack Lattice

Vincent Mellor (2010). Numerical Simulations of the Ising Model on the Union Jack Lattice PhD Thesis, School of Mathematics & Physics, The University of Queensland.

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Author Vincent Mellor
Thesis Title Numerical Simulations of the Ising Model on the Union Jack Lattice
School, Centre or Institute School of Mathematics & Physics
Institution The University of Queensland
Publication date 2010-11-18
Thesis type PhD Thesis
Total pages 156
Total colour pages 31
Total black and white pages 125
Subjects 01 Mathematical Sciences
Abstract/Summary The Ising model is famous model for magnetic substances in Statistical Physics, and has been greatly studied in many forms. It was solved in one-dimension by Ernst Ising in 1925 and in two-dimensions without an external magnetic field by Lars Onsager in 1944. In this thesis we look at the anisotropic Ising model on the Union Jack lattice. This lattice is one of the few exactly solvable models which exhibits a re-entrant phase transition and so is of great interest. Initially we cover the history of the Ising model and some possible applications outside the traditional magnetic substances. Background theory will be presented before briefly discussing the calculations for the one-dimensional and two-dimensional models. After this we will focus on the Union Jack lattice and specifically the work of Wu and Lin in their 1987 paper “Ising model on the Union Jack lattice as a free fermion model.” [WL87]. Next we will develop a mean field prediction for the Union Jack lattice after first discussing mean field theory for other lattices. Finally we will present the results of numerical simulations. These simulations will be performed using a Monte Carlo method, specifically the Metropolis-Hastings algorithm, to simulate a Markov chain. Initially we calibrate our simulation program using the triangular lattice, before going on to run simulations for Ferromagnetic, Antiferromagnetic and Metamagnetic systems on the Union Jack lattice.
Keyword Ising Model
Statistical mechanics
Monte Carlo simulation
Additional Notes Colour pages: 18,33,38,49,53,61-67,79,81-85,94-97,100-107,122

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Created: Thu, 18 Nov 2010, 23:24:26 EST by Mr Vincent Mellor on behalf of Library - Information Access Service