• Introduction
• Themes
• Condsened Matter Systems
• Chapter 1: The Long Range Falikov-Kimball Model
• Contributions
• Introduction
• Localisation
• Falikov Kimball and Hubbard models
• Localisation
• Numerical Methods
• Markov Chain Monte-Carlo in Practice}
• Introduction
• The Long-Ranged Falikov-Kimball Model
• The Phase Diagram
• Markov Chain Monte Carlo and Emergent Disorder
• Localisation Properties
• Discussion & Conclusion
• Acknowledgments
• []{#app:balance label="app:balance"} DETAILED BALANCE
• []{#app:disorder_model label="app:disorder_model"} UNCORRELATED DISORDER MODEL
• Chapter 2: The Amorphous Kitaev Model
• Contributions
• Introduction
• Amorphous Systems
• Glossary
• The Kitaev Model
• The Majorana Hamiltonian
• Gauge Fields
• The Projector
• The Ground State
• Phases of the Kitaev Model
• What is so great about two dimensions?
• Methods
• Voronisation
• Graph Representation
• Colouring the Bonds
• Mapping between flux sectors and bond sectors
• Chern Markers
• Results
• The Ground State Flux Sector
• Spontaneous Chiral Symmetry Breaking
• Ground State Phase Diagram
• Anderson Transition to a Thermal Metal
• Conclusion
• Discussion
• Limits of the ground state conjecture
• Outlook
• Experimental Realisations and Signatures
• Generalisations
• Conclusion
• Discussion
• Future Work