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On classical and quantum lattice spin systems
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Benassi, Costanza (2018) On classical and quantum lattice spin systems. PhD thesis, University of Warwick.
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WRAP_Theses_Benassi_2018.pdf - Submitted Version - Requires a PDF viewer. Download (1222Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3226378~S15
Abstract
This thesis focuses on some results about quantum and classical lattice spin systems. We study a wide class of two-dimensional quantum models which enjoy a U(1) symmetry. Using the so called complex rotation method we show that the decay of the relevant correlation functions is at least algebraically fast. We provide some examples of relevant models which belong to our class.
We review some results present in the literature concerning the so called GriffthsGinibre inequalities for the classical XY model and propose a generalisation to its quantum counterpart. Correlation inequalities indeed hold for the quantum XY model with spin- 1 2 and for the ground state of the spin-1 system. We propose some applications of these results, namely that the infinite volume limit of some correlation functions exists and that it is possible to compare quenched and annealed averages for a quantum XY model with random couplings.
We investigate loop representations for O(n) classical spin systems. We propose a generalised random current representation and show its relationship with the Brydges-Fröhlich-Spencer one. We review some conjectures regarding the expected behaviour of these loop models { namely that macroscopic loops appear and their lengths are distributed according to a Poisson-Dirichlet distribution. We propose some arguments in favour of these conjectures for O(n) loop models, using a mix of exact results and heuristic considerations. In order to do so we de ne a stochastic process which is an effective split-merge process for macroscopic loops and we reformulate some correlation functions for the O(2) spin system in terms of loop properties.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QC Physics | ||||
| Library of Congress Subject Headings (LCSH): | Quantum theory, Nuclear spin, Poisson distribution | ||||
| Official Date: | May 2018 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Ueltschi, Daniel, 1969- | ||||
| Extent: | 136 leaves : charts | ||||
| Language: | eng |
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