Double tangent method for two-periodic Aztec diamonds
We use the octahedron recurrence, which generalizes the quadratic recurrence found by Kuo for standard Aztec diamonds, in order to compute boundary one-refined and two-refined partition functions for two-periodic Aztec diamonds. In a first approach, the geometric tangent method allows to derive the...
Published in: | Journal of Statistical Mechanics: Theory and Experiment |
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2022
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ftunistlouisbrus:oai:dial.uclouvain.be:boreal:268643 2024-05-12T07:58:52+00:00 Double tangent method for two-periodic Aztec diamonds Ruelle, Philippe UCL - SST/IRMP - Institut de recherche en mathématique et physique 2022 http://hdl.handle.net/2078.1/268643 https://doi.org/10.1088/1742-5468/aca4c4 eng eng Institute of Physics Publishing Ltd. boreal:268643 http://hdl.handle.net/2078.1/268643 doi:10.1088/1742-5468/aca4c4 urn:EISSN:1742-5468 info:eu-repo/semantics/openAccess Journal of Statistical Mechanics: Theory and Experiment, Vol. , no.12, p. 123103 (2022) arctic curves tangent method domino tilings Aztec diamonds octahedron recurremce info:eu-repo/semantics/article 2022 ftunistlouisbrus https://doi.org/10.1088/1742-5468/aca4c4 2024-04-18T17:09:55Z We use the octahedron recurrence, which generalizes the quadratic recurrence found by Kuo for standard Aztec diamonds, in order to compute boundary one-refined and two-refined partition functions for two-periodic Aztec diamonds. In a first approach, the geometric tangent method allows to derive the parametric form of the arctic curve, separating the solid and liquid phases. This is done by using the recent reformulation of the tangent method and the one-refined partition functions without extension of the domain. In a second part, we use the two-refined tangent method to rederive the arctic curve from the boundary two-refined partition functions, which we compute exactly on the lattice. The curve satisfies the known algebraic equation of degree 8, of which either tangent method gives an explicit parametrization. Article in Journal/Newspaper Arctic DIAL@USL-B (Université Saint-Louis, Bruxelles) Arctic Journal of Statistical Mechanics: Theory and Experiment 2022 12 123103 |
institution |
Open Polar |
collection |
DIAL@USL-B (Université Saint-Louis, Bruxelles) |
op_collection_id |
ftunistlouisbrus |
language |
English |
topic |
arctic curves tangent method domino tilings Aztec diamonds octahedron recurremce |
spellingShingle |
arctic curves tangent method domino tilings Aztec diamonds octahedron recurremce Ruelle, Philippe Double tangent method for two-periodic Aztec diamonds |
topic_facet |
arctic curves tangent method domino tilings Aztec diamonds octahedron recurremce |
description |
We use the octahedron recurrence, which generalizes the quadratic recurrence found by Kuo for standard Aztec diamonds, in order to compute boundary one-refined and two-refined partition functions for two-periodic Aztec diamonds. In a first approach, the geometric tangent method allows to derive the parametric form of the arctic curve, separating the solid and liquid phases. This is done by using the recent reformulation of the tangent method and the one-refined partition functions without extension of the domain. In a second part, we use the two-refined tangent method to rederive the arctic curve from the boundary two-refined partition functions, which we compute exactly on the lattice. The curve satisfies the known algebraic equation of degree 8, of which either tangent method gives an explicit parametrization. |
author2 |
UCL - SST/IRMP - Institut de recherche en mathématique et physique |
format |
Article in Journal/Newspaper |
author |
Ruelle, Philippe |
author_facet |
Ruelle, Philippe |
author_sort |
Ruelle, Philippe |
title |
Double tangent method for two-periodic Aztec diamonds |
title_short |
Double tangent method for two-periodic Aztec diamonds |
title_full |
Double tangent method for two-periodic Aztec diamonds |
title_fullStr |
Double tangent method for two-periodic Aztec diamonds |
title_full_unstemmed |
Double tangent method for two-periodic Aztec diamonds |
title_sort |
double tangent method for two-periodic aztec diamonds |
publisher |
Institute of Physics Publishing Ltd. |
publishDate |
2022 |
url |
http://hdl.handle.net/2078.1/268643 https://doi.org/10.1088/1742-5468/aca4c4 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
Journal of Statistical Mechanics: Theory and Experiment, Vol. , no.12, p. 123103 (2022) |
op_relation |
boreal:268643 http://hdl.handle.net/2078.1/268643 doi:10.1088/1742-5468/aca4c4 urn:EISSN:1742-5468 |
op_rights |
info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.1088/1742-5468/aca4c4 |
container_title |
Journal of Statistical Mechanics: Theory and Experiment |
container_volume |
2022 |
container_issue |
12 |
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123103 |
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1798839491688923136 |