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Phase transitions and the random-cluster representation for Delaunay Potts models with geometry-dependent interactions
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Nollett, William R. (2013) Phase transitions and the random-cluster representation for Delaunay Potts models with geometry-dependent interactions. PhD thesis, University of Warwick.
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WRAP_THESIS_Nollett_2013.pdf - Submitted Version - Requires a PDF viewer. Download (965Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b2724083~S1
Abstract
We investigate the existence of phase transitions for a class of continuum multi-type
particle systems. The interactions act on hyperedges between the particles, allowing
us to define a class of models with geometry-dependent interactions. We establish
the existence of stationary Gibbsian point processes for this class of models. A
phase transition is defined with respect to the existence of multiple Gibbs measures,
and we establish the existence of phase transitions in our models by proving that
multiple Gibbs measures exist.
Our approach involves introducing a random-cluster representation for continuum
particle systems with geometry-dependent interactions. We then argue that
percolation in the random-cluster model corresponds to the existence of a phase transition.
The originality in this research is defining a random-cluster representation
for continuum models with hyperedge interactions, and applying this representation
in order to show the existence of a phase transition.
We mainly focus on models where the interaction is defined in terms of the
Delaunay hypergraph. We find that phase transitions exist for a class of models
where the interaction between particles is via Delaunay edges or Delaunay triangles.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Library of Congress Subject Headings (LCSH): | Phase transformations (Statistical physics), Gibbs' equation, Particles, Continuum mechanics | ||||
Official Date: | September 2013 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Adams, S. (Stefan) | ||||
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC); University of Warwick | ||||
Extent: | v, 125 pages. | ||||
Language: | eng |
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