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The statistical physics of the 1-D to 2-D crossover using transfer function techniques

Cave, Andrew M. (2016)
Ph.D. thesis, University of Birmingham.

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Abstract

We develop a novel technique that allows us to directly probe the thermodynamics of the two dimensional limit of the nearest neighbour square lattice clock model. It is a process that uses exact diagonalisation techniques through the use of transfer functions. It is conceptually easy to understand as an extension of the transfer matrices used to solve the 1D Ising model and other similar Hamiltonians. This transfer function technique is applied to a set of 1D spiral geometries with increasing radius N. In the limit N → ∞ the spiral becomes the square lattice and our results are interpreted with respect to this limit. We present convincing evidence that the two transitions that are exhibited in the p
> 4 clock model have singular behaviour and above a certain temperature between the transitions convergently behave like the plane rotator model.

Type of Work:Ph.D. thesis.
Supervisor(s):Long, Martin
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Physics and Astronomy
Subjects:QC Physics
Institution:University of Birmingham
ID Code:6464
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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