Topological sectors, dimer correlations, and monomers from the transfer-matrix solution of the dimer model

Wilkins, Neil; Powell, Stephen

Abstract

We solve the classical square-lattice dimer model with periodic boundaries and in the presence of a field t that couples to the (vector) flux, by diagonalizing a modified version of Lieb's transfer matrix. After deriving the torus partition function in the thermodynamic limit, we show how the configuration space divides into topological sectors corresponding to distinct values of the flux. Additionally, we demonstrate in general that expectation values are t independent at leading order, and obtain explicit expressions for dimer occupation numbers, dimer-dimer correlation functions, and the monomer distribution function. The last of these is expressed as a Toeplitz determinant, whose asymptotic behavior for large monomer separation is tractable using the Fisher-Hartwig conjecture. Our results reproduce those previously obtained using Pfaffian techniques.

Citation

Wilkins, N., & Powell, S. (2021). Topological sectors, dimer correlations, and monomers from the transfer-matrix solution of the dimer model. Physical Review E, 104(1), Article 014145. https://doi.org/10.1103/physreve.104.014145

• Journal Article Type: Article
• Acceptance Date: Jun 29, 2021
• Online Publication Date: Jul 29, 2021
• Publication Date: Jul 29, 2021
• Deposit Date: Jul 14, 2021
• Publicly Available Date: Jul 29, 2021
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 104
• Issue: 1
• Article Number: 014145
• DOI: https://doi.org/10.1103/physreve.104.014145
• Public URL: https://nottingham-repository.worktribe.com/output/5763206
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.014145