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

Wilkins, Neil; Powell, Stephen

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


Authors

Neil Wilkins



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.

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 (APS)
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

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