Arctic curves of the twenty-vertex model with domain wall boundaries
We use the tangent method to compute the arctic curve of the Twenty-Vertex (20V) model with particular domain wall boundary conditions for a wide set of integrable weights. To this end, we extend to the finite geometry of domain wall boundary conditions the standard connection between the bulk 20V a...
Published in: | Journal of Statistical Physics |
---|---|
Main Authors: | , , |
Other Authors: | |
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
Springer Science and Business Media LLC
2020
|
Subjects: | |
Online Access: | http://hdl.handle.net/2078.1/250661 https://doi.org/10.1007/s10955-020-02518-y |
id |
ftunistlouisbrus:oai:dial.uclouvain.be:boreal:250661 |
---|---|
record_format |
openpolar |
spelling |
ftunistlouisbrus:oai:dial.uclouvain.be:boreal:250661 2024-05-12T07:58:25+00:00 Arctic curves of the twenty-vertex model with domain wall boundaries Debin, Bryan Di Francesco, Philippe Guitter, Emmanuel UCL - SST/IRMP - Institut de recherche en mathématique et physique 2020 http://hdl.handle.net/2078.1/250661 https://doi.org/10.1007/s10955-020-02518-y eng eng Springer Science and Business Media LLC boreal:250661 http://hdl.handle.net/2078.1/250661 doi:10.1007/s10955-020-02518-y urn:ISSN:0022-4715 urn:EISSN:1572-9613 info:eu-repo/semantics/openAccess Journal of Statistical Physics, Vol. 179, no.1, p. 33-89 (2020) Mathematical Physics Statistical and Nonlinear Physics info:eu-repo/semantics/article 2020 ftunistlouisbrus https://doi.org/10.1007/s10955-020-02518-y 2024-04-18T17:16:09Z We use the tangent method to compute the arctic curve of the Twenty-Vertex (20V) model with particular domain wall boundary conditions for a wide set of integrable weights. To this end, we extend to the finite geometry of domain wall boundary conditions the standard connection between the bulk 20V and 6V models via the Kagome lattice ice model. This allows to express refined partition functions of the 20V model in terms of their 6V counterparts, leading to explicit parametric expressions for the various portions of its arctic curve. The latter displays a large variety of shapes depending on the weights and separates a central liquid phase from up to six different frozen phases. A number of numerical simulations are also presented, which highlight the arctic curve phenomenon and corroborate perfectly the analytic predictions of the tangent method. We finally compute the arctic curve of the Quarter Turn symmetric Holey Aztec Domino Tiling (QTHADT) model, a problem closely related to the 20V model and whose asymptotics may be analyzed via a similar tangent method approach. Again results for the QTHADT model are found to be in perfect agreement with our numerical simulations. Article in Journal/Newspaper Arctic DIAL@USL-B (Université Saint-Louis, Bruxelles) Arctic Journal of Statistical Physics 179 1 33 89 |
institution |
Open Polar |
collection |
DIAL@USL-B (Université Saint-Louis, Bruxelles) |
op_collection_id |
ftunistlouisbrus |
language |
English |
topic |
Mathematical Physics Statistical and Nonlinear Physics |
spellingShingle |
Mathematical Physics Statistical and Nonlinear Physics Debin, Bryan Di Francesco, Philippe Guitter, Emmanuel Arctic curves of the twenty-vertex model with domain wall boundaries |
topic_facet |
Mathematical Physics Statistical and Nonlinear Physics |
description |
We use the tangent method to compute the arctic curve of the Twenty-Vertex (20V) model with particular domain wall boundary conditions for a wide set of integrable weights. To this end, we extend to the finite geometry of domain wall boundary conditions the standard connection between the bulk 20V and 6V models via the Kagome lattice ice model. This allows to express refined partition functions of the 20V model in terms of their 6V counterparts, leading to explicit parametric expressions for the various portions of its arctic curve. The latter displays a large variety of shapes depending on the weights and separates a central liquid phase from up to six different frozen phases. A number of numerical simulations are also presented, which highlight the arctic curve phenomenon and corroborate perfectly the analytic predictions of the tangent method. We finally compute the arctic curve of the Quarter Turn symmetric Holey Aztec Domino Tiling (QTHADT) model, a problem closely related to the 20V model and whose asymptotics may be analyzed via a similar tangent method approach. Again results for the QTHADT model are found to be in perfect agreement with our numerical simulations. |
author2 |
UCL - SST/IRMP - Institut de recherche en mathématique et physique |
format |
Article in Journal/Newspaper |
author |
Debin, Bryan Di Francesco, Philippe Guitter, Emmanuel |
author_facet |
Debin, Bryan Di Francesco, Philippe Guitter, Emmanuel |
author_sort |
Debin, Bryan |
title |
Arctic curves of the twenty-vertex model with domain wall boundaries |
title_short |
Arctic curves of the twenty-vertex model with domain wall boundaries |
title_full |
Arctic curves of the twenty-vertex model with domain wall boundaries |
title_fullStr |
Arctic curves of the twenty-vertex model with domain wall boundaries |
title_full_unstemmed |
Arctic curves of the twenty-vertex model with domain wall boundaries |
title_sort |
arctic curves of the twenty-vertex model with domain wall boundaries |
publisher |
Springer Science and Business Media LLC |
publishDate |
2020 |
url |
http://hdl.handle.net/2078.1/250661 https://doi.org/10.1007/s10955-020-02518-y |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
Journal of Statistical Physics, Vol. 179, no.1, p. 33-89 (2020) |
op_relation |
boreal:250661 http://hdl.handle.net/2078.1/250661 doi:10.1007/s10955-020-02518-y urn:ISSN:0022-4715 urn:EISSN:1572-9613 |
op_rights |
info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.1007/s10955-020-02518-y |
container_title |
Journal of Statistical Physics |
container_volume |
179 |
container_issue |
1 |
container_start_page |
33 |
op_container_end_page |
89 |
_version_ |
1798838847770984448 |