Arctic curves of the octahedron equation
PACS numbers: 64.60.De, 64.70.qd, 02.10.Ox International audience We study the octahedron relation (also known as the $A_{\infty}$ $T$-system), obeyed in particular by the partition function for dimer coverings of the Aztec Diamond graph. For a suitable class of doubly periodic initial conditions, w...
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ftceafr:oai:HAL:cea-01002519v1 2024-09-09T19:20:22+00:00 Arctic curves of the octahedron equation Di Francesco, P. Soto-Garrido, R. Department of Mathematics Urbana University of Illinois at Urbana-Champaign Urbana (UIUC) University of Illinois System-University of Illinois System Institut de Physique Théorique - UMR CNRS 3681 (IPHT) Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)) Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA) Department of Physics Illinois at Urbana-Champaign, USA 2014 https://cea.hal.science/cea-01002519 https://doi.org/10.1088/1751-8113/47/28/285204 en eng HAL CCSD IOP Publishing info:eu-repo/semantics/altIdentifier/arxiv/1402.4493 info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/47/28/285204 cea-01002519 https://cea.hal.science/cea-01002519 ARXIV: 1402.4493 doi:10.1088/1751-8113/47/28/285204 ISSN: 1751-8113 EISSN: 1751-8121 Journal of Physics A: Mathematical and Theoretical https://cea.hal.science/cea-01002519 Journal of Physics A: Mathematical and Theoretical, 2014, 47 (28), pp.285204. ⟨10.1088/1751-8113/47/28/285204⟩ arctic curve dimer tiling exact solution phase transition [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] info:eu-repo/semantics/article Journal articles 2014 ftceafr https://doi.org/10.1088/1751-8113/47/28/285204 2024-07-22T13:32:37Z PACS numbers: 64.60.De, 64.70.qd, 02.10.Ox International audience We study the octahedron relation (also known as the $A_{\infty}$ $T$-system), obeyed in particular by the partition function for dimer coverings of the Aztec Diamond graph. For a suitable class of doubly periodic initial conditions, we find exact solutions with a particularly simple factorized form. For these, we show that the density function that measures the average dimer occupation of a face of the Aztec graph, obeys a system of linear recursion relations with periodic coefficients. This allows us to explore the thermodynamic limit of the corresponding dimer models and to derive exact "arctic" curves separating the various phases of the system. Article in Journal/Newspaper Arctic HAL-CEA (Commissariat à l'énergie atomique et aux énergies alternatives) Arctic Journal of Physics A: Mathematical and Theoretical 47 28 285204 |
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HAL-CEA (Commissariat à l'énergie atomique et aux énergies alternatives) |
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English |
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arctic curve dimer tiling exact solution phase transition [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] |
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arctic curve dimer tiling exact solution phase transition [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Di Francesco, P. Soto-Garrido, R. Arctic curves of the octahedron equation |
topic_facet |
arctic curve dimer tiling exact solution phase transition [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] |
description |
PACS numbers: 64.60.De, 64.70.qd, 02.10.Ox International audience We study the octahedron relation (also known as the $A_{\infty}$ $T$-system), obeyed in particular by the partition function for dimer coverings of the Aztec Diamond graph. For a suitable class of doubly periodic initial conditions, we find exact solutions with a particularly simple factorized form. For these, we show that the density function that measures the average dimer occupation of a face of the Aztec graph, obeys a system of linear recursion relations with periodic coefficients. This allows us to explore the thermodynamic limit of the corresponding dimer models and to derive exact "arctic" curves separating the various phases of the system. |
author2 |
Department of Mathematics Urbana University of Illinois at Urbana-Champaign Urbana (UIUC) University of Illinois System-University of Illinois System Institut de Physique Théorique - UMR CNRS 3681 (IPHT) Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)) Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA) Department of Physics Illinois at Urbana-Champaign, USA |
format |
Article in Journal/Newspaper |
author |
Di Francesco, P. Soto-Garrido, R. |
author_facet |
Di Francesco, P. Soto-Garrido, R. |
author_sort |
Di Francesco, P. |
title |
Arctic curves of the octahedron equation |
title_short |
Arctic curves of the octahedron equation |
title_full |
Arctic curves of the octahedron equation |
title_fullStr |
Arctic curves of the octahedron equation |
title_full_unstemmed |
Arctic curves of the octahedron equation |
title_sort |
arctic curves of the octahedron equation |
publisher |
HAL CCSD |
publishDate |
2014 |
url |
https://cea.hal.science/cea-01002519 https://doi.org/10.1088/1751-8113/47/28/285204 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
ISSN: 1751-8113 EISSN: 1751-8121 Journal of Physics A: Mathematical and Theoretical https://cea.hal.science/cea-01002519 Journal of Physics A: Mathematical and Theoretical, 2014, 47 (28), pp.285204. ⟨10.1088/1751-8113/47/28/285204⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/arxiv/1402.4493 info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/47/28/285204 cea-01002519 https://cea.hal.science/cea-01002519 ARXIV: 1402.4493 doi:10.1088/1751-8113/47/28/285204 |
op_doi |
https://doi.org/10.1088/1751-8113/47/28/285204 |
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Journal of Physics A: Mathematical and Theoretical |
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47 |
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28 |
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285204 |
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1809760507392950272 |