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Field correlations in Coulomb gases

Gray, Callum; (2019) Field correlations in Coulomb gases. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The Coulomb gas is a ubiquitous concept not just in physics but in many other fields of science, including chemistry, biology and engineering. In this thesis I make use the concept of the ``generalised'' Coulomb gas, which extends the concept of the ``traditional'' Coulomb gas by allowing more general solutions to Gauss' law without changing its fundamental thermodynamic properties. The generalised Coulomb gas was first introduced by Maggs and collaborators, who used it to develop a fast local simulation algorithm for Coulombic systems by taking advantage of the fact that the thermodynamics are unchanged. Further studies were conducted by Faulkner, who studied the generalised Coulomb gas not just for its intrinsic interest but also in the context of the XY model of magnetism, which maps to a 2D generalised Coulomb gas. I perform numerical studies of the generalised Coulomb gas, paying particular attention to the calculation of its field correlations; surprisingly, these have not been supplied before in the literature. These correlations can be separated into Helmholtz-decomposed components in order to extract the correlations of the traditional Coulomb gas, which are contained within those of the generalised system. I calculate field correlations in the 2D generalised Coulomb gas in the grand canonical ensemble in all regions of its phase diagram, which was given by Lee and Teitel and includes two Berezinskii-Kosterlitz-Thouless transitions, a first-order gas-solid transition and an Ising solid-liquid transition. I also perform analogous simulations of the harmonic XY model of magnetism, following the work of Faulkner, and show that it is the generalised Coulomb gas rather than the traditional one which provides a natural description of the emergent Coulomb physics therein. Lastly, I show preliminary simulations of the 2D canonical and 3D grand canonical generalised lattice Coulomb gases on the square and simple cubic lattices respectively, and suggest further work, including the possibility of performing simulations on the diamond lattice in order to make closer contact with spin ice physics.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Field correlations in Coulomb gases
Event: UCL (University College London)
Language: English
Additional information: Copyright © The Author 2019. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request.
Keywords: Correlations, Coulomb gases, Emergent phenomena
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > London Centre for Nanotechnology
URI: http://discovery.ucl.ac.uk/id/eprint/10067492
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