Exact solution to the quantum and classical dimer models on the spectre aperiodic monotiling

Singh, Shobhna and Flicker, Felix ORCID: https://orcid.org/0000-0002-8362-1384 2024. Exact solution to the quantum and classical dimer models on the spectre aperiodic monotiling. Physical Review B (condensed matter and materials physics) 109 (22) , L220303. 10.1103/PhysRevB.109.L220303

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Abstract

The decades-long search for a shape that tiles the plane only aperiodically under translations and rotations recently ended with the discovery of the “spectre” aperiodic monotile. In this setting we study the dimer model, in which dimers are placed along tile edges such that each vertex meets precisely one dimer. The complexity of the tiling combines with the dimer constraint to allow an exact solution to the model. The partition function is

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Physics and Astronomy
Publisher:	American Physical Society
ISSN:	2469-9950
Date of First Compliant Deposit:	28 June 2024
Date of Acceptance:	3 June 2024
Last Modified:	02 Jul 2024 15:00
URI:	https://orca.cardiff.ac.uk/id/eprint/170165

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