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Title: Correlations in geometrically frustrated spin systems
Author: Hogan, Patrick
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2006
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In this thesis we study the quantum and statistical mechanics of geometrically frustrated antiferromagnets. In particular, we develop a novel, general approach for studying the disordered phases of systems comprised of vertex-sharing fully frustrated spin clusters, in which every pair of spins is coupled equally by antiferromagnetic Heisenberg interactions. The novel feature of our approach is the use of conjugate Hubbard-Stratonovich fields associated with each fully frustrated cluster of spins, rather than with the spin sites themselves, to decouple all the individual spin-spin exchange interactions in the system. The individual spins in the system may then be integrated out, leaving behind a conjugate lattice of conjugate fields, coupled to each other through the spin-sites that were common to neighbouring clusters. By investigating the behaviour of these remaining conjugate fields, we may probe the properties and behaviour of the original system, and we hope this novel approach will provide a framework for a better theoretical understanding of such frustrated systems. One of the key strengths of our conjugate-field approach is the ability to make controlled, accurate approximations about the ground state in geometrically frustrated systems which support large low-temperature spin fluctuations, due to the presence of a barrierless, massively degenerate ground-state manifold. This is possible as our Hubbard-Stratonovich fields are conjugate to our spins, and so have correspondingly only small fluctuations about their ground-state. We first introduce our conjugate-field approach by studying the quantum mechanics of a single fully frustrated cluster of spins, for which we recover an exact expression for the finite-temperature partition function as a finite sum of single integrals. Extending our approach to treat more complex frustrated systems of coupled clusters, we find that the clusters are decoupled by different conjugate fields which have partial correlations. This complicates the implementation of our approach considerably, and the remainder of the thesis focuses on how we may make controlled approximations to recover correlation functions in such systems in both the classical and quantum limits.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available