Miquel dynamics, Clifford lattices and the Dimer model

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dc.contributor.authorAffolter, Niklas C.
dc.date.accessioned2021-05-28T08:00:45Z
dc.date.available2021-05-28T08:00:45Z
dc.date.issued2021-05-02
dc.description.abstractMiquel dynamics was introduced by Ramassamy as a discrete time evolution of square grid circle patterns on the torus. In each time step every second circle in the pattern is replaced with a new one by employing Miquel’s six circle theorem. Inspired by this dynamics we consider the local Miquel move, which changes the combinatorics and geometry of a circle pattern. We prove that the circle centers under Miquel dynamics are Clifford lattices, an integrable system considered by Konopelchenko and Schief. Clifford lattices have the combinatorics of an octahedral lattice, and every octahedron contains six intersection points of Clifford’s four circle configuration. The Clifford move replaces one of these circle intersection points with the opposite one. We establish a new connection between circle patterns and the dimer model: If the distances between circle centers are interpreted as edge weights, the Miquel move preserves probabilities in the sense of urban renewal.en
dc.description.sponsorshipTU Berlin, Open-Access-Mittel – 2021en
dc.description.sponsorshipDFG, 195170736, TRR 109: Diskretisierung in Geometrie und Dynamiken
dc.identifier.eissn1573-0530
dc.identifier.issn0377-9017
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/13162
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-11956
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc530 Physikde
dc.subject.otherMiquel dynamicsen
dc.subject.othercircle patternsen
dc.subject.otherClifford latticesen
dc.subject.otherDimer modelen
dc.subject.otherurban renewalen
dc.titleMiquel dynamics, Clifford lattices and the Dimer modelen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.articlenumber61en
dcterms.bibliographicCitation.doi10.1007/s11005-021-01406-0en
dcterms.bibliographicCitation.journaltitleLetters in mathematical physicsen
dcterms.bibliographicCitation.originalpublishernameSpringer Natureen
dcterms.bibliographicCitation.originalpublisherplaceHeidelbergen
dcterms.bibliographicCitation.volume111en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Diskrete Mathematik / Geometriede
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Diskrete Mathematik / Geometriede
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen

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