Arctic curves of the twenty-vertex model with domain wall boundaries
68 pages, 37 figures International audience 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 th...
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ftccsdartic:oai:HAL:cea-02932213v1 2023-05-15T14:43:54+02:00 Arctic curves of the twenty-vertex model with domain wall boundaries Debin, Bryan Di Francesco, Philippe Guitter, Emmanuel Institut de Recherche en Mathématiques et Physique (UCL IRMP) Université Catholique de Louvain = Catholic University of Louvain (UCL) Institut de Physique Théorique - UMR CNRS 3681 (IPHT) Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) Department of Mathematics, Illinois State University Illinois State University Université Paris-Saclay Fonds National de la Recherche Scientifique The Fonds Wetenschappelijk Onderzoek ANR-14-CE25-0014,GRAAL,GRaphes et Arbres ALéatoires(2014) 2020 https://hal-cea.archives-ouvertes.fr/cea-02932213 https://hal-cea.archives-ouvertes.fr/cea-02932213/document https://hal-cea.archives-ouvertes.fr/cea-02932213/file/1910.06833.pdf https://doi.org/10.1007/s10955-020-02518-y en eng HAL CCSD Springer Verlag info:eu-repo/semantics/altIdentifier/arxiv/1910.06833 info:eu-repo/semantics/altIdentifier/doi/10.1007/s10955-020-02518-y cea-02932213 https://hal-cea.archives-ouvertes.fr/cea-02932213 https://hal-cea.archives-ouvertes.fr/cea-02932213/document https://hal-cea.archives-ouvertes.fr/cea-02932213/file/1910.06833.pdf ARXIV: 1910.06833 doi:10.1007/s10955-020-02518-y info:eu-repo/semantics/OpenAccess ISSN: 0022-4715 EISSN: 1572-9613 Journal of Statistical Physics https://hal-cea.archives-ouvertes.fr/cea-02932213 Journal of Statistical Physics, Springer Verlag, 2020, 179, pp.33-89. ⟨10.1007/s10955-020-02518-y⟩ [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] info:eu-repo/semantics/article Journal articles 2020 ftccsdartic https://doi.org/10.1007/s10955-020-02518-y 2021-12-19T00:57:02Z 68 pages, 37 figures International audience 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 Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) Arctic Journal of Statistical Physics 179 1 33 89 |
institution |
Open Polar |
collection |
Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
op_collection_id |
ftccsdartic |
language |
English |
topic |
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] |
spellingShingle |
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] Debin, Bryan Di Francesco, Philippe Guitter, Emmanuel Arctic curves of the twenty-vertex model with domain wall boundaries |
topic_facet |
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] |
description |
68 pages, 37 figures International audience 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 |
Institut de Recherche en Mathématiques et Physique (UCL IRMP) Université Catholique de Louvain = Catholic University of Louvain (UCL) Institut de Physique Théorique - UMR CNRS 3681 (IPHT) Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) Department of Mathematics, Illinois State University Illinois State University Université Paris-Saclay Fonds National de la Recherche Scientifique The Fonds Wetenschappelijk Onderzoek ANR-14-CE25-0014,GRAAL,GRaphes et Arbres ALéatoires(2014) |
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 |
HAL CCSD |
publishDate |
2020 |
url |
https://hal-cea.archives-ouvertes.fr/cea-02932213 https://hal-cea.archives-ouvertes.fr/cea-02932213/document https://hal-cea.archives-ouvertes.fr/cea-02932213/file/1910.06833.pdf https://doi.org/10.1007/s10955-020-02518-y |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
ISSN: 0022-4715 EISSN: 1572-9613 Journal of Statistical Physics https://hal-cea.archives-ouvertes.fr/cea-02932213 Journal of Statistical Physics, Springer Verlag, 2020, 179, pp.33-89. ⟨10.1007/s10955-020-02518-y⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/arxiv/1910.06833 info:eu-repo/semantics/altIdentifier/doi/10.1007/s10955-020-02518-y cea-02932213 https://hal-cea.archives-ouvertes.fr/cea-02932213 https://hal-cea.archives-ouvertes.fr/cea-02932213/document https://hal-cea.archives-ouvertes.fr/cea-02932213/file/1910.06833.pdf ARXIV: 1910.06833 doi:10.1007/s10955-020-02518-y |
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 |
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1766315474061099008 |