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Title: Exotic order in magnetic systems from Majorana fermions
Author: Bennett, Edmund
ISNI:       0000 0004 5921 5268
Awarding Body: University of St Andrews
Current Institution: University of St Andrews
Date of Award: 2016
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This thesis explores the theoretical representation of localised electrons in magnetic systems, using Majorana fermions. A motivation is provided for the Majorana fermion representation, which is then developed and applied as a mean-field theory and in the path-integral formalism to the Ising model in transversal-field (TFIM) in one, two and three dimensions, on an orthonormal lattice. In one dimension the development of domain walls precludes long-range order in discrete systems; this is as free energy savings due to entropy outweigh the energetic cost of a domain wall. An argument due to Peierls exists in 2D which allows the formation of domains of ordered spins amidst a disordered background, however, which may be extended to 3D. The forms of the couplings to the bosons used in the Random Phase Analysis (RPA) are considered and an explanation for the non-existence of the phases calculated in this thesis is discussed, in terms of spare degrees of freedom in the Majorana representation. This thesis contains the first known application of Majorana fermions at the RPA level.
Supervisor: Hooley, Chris Sponsor: Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Majorana ; Magnetism ; Quantum field theory ; Ising ; Path integral ; Random phase approximation ; QC174.45B4 ; Electrons ; Fermions ; Ising model ; Path integrals