Arctic curves of the T-system with Slanted Initial Data ...
We study the T-system of type $A_\infty$, also known as the octahedron recurrence/equation, viewed as a 2+1-dimensional discrete evolution equation. Generalizing the study of [P. Di Francesco and R. Soto-Garrido. Arctic curves of the octahedron equation. J. Phys. A, 47(28):285204, 34, 2014], we cons...
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ftdatacite:10.48550/arxiv.2403.02479 2024-09-09T19:21:08+00:00 Arctic curves of the T-system with Slanted Initial Data ... Di Francesco, Philippe Vu, Hieu Trung 2024 https://dx.doi.org/10.48550/arxiv.2403.02479 https://arxiv.org/abs/2403.02479 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Mathematical Physics math-ph Statistical Mechanics cond-mat.stat-mech Combinatorics math.CO FOS Physical sciences FOS Mathematics article Article Preprint CreativeWork 2024 ftdatacite https://doi.org/10.48550/arxiv.2403.02479 2024-08-01T11:49:18Z We study the T-system of type $A_\infty$, also known as the octahedron recurrence/equation, viewed as a 2+1-dimensional discrete evolution equation. Generalizing the study of [P. Di Francesco and R. Soto-Garrido. Arctic curves of the octahedron equation. J. Phys. A, 47(28):285204, 34, 2014], we consider initial data along parallel ``slanted" planes perpendicular to an arbitrary admissible direction $(r,s,t)\in {\mathbb Z}_+^3$. The solution of the T-system is interpreted as the partition function of a dimer model on some suitable ``pinecone" graph introduced in [M. Bousquet-Mélou, J. Propp, and J. West. Perfect matchings for the three-term Gale-Robinson sequences. Electron. J. Combin., 16(1):Research Paper 125, 37, 2009]. The T-system formulation and some exact solutions in uniform or periodic cases allow us to explore the thermodynamic limit of the corresponding dimer models and to derive exact arctic curves separating the various phases of the system. ... : 69 pages, 42 figures ... Report Arctic DataCite Arctic Garrido ENVELOPE(-57.067,-57.067,-63.500,-63.500) |
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op_collection_id |
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topic |
Mathematical Physics math-ph Statistical Mechanics cond-mat.stat-mech Combinatorics math.CO FOS Physical sciences FOS Mathematics |
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Mathematical Physics math-ph Statistical Mechanics cond-mat.stat-mech Combinatorics math.CO FOS Physical sciences FOS Mathematics Di Francesco, Philippe Vu, Hieu Trung Arctic curves of the T-system with Slanted Initial Data ... |
topic_facet |
Mathematical Physics math-ph Statistical Mechanics cond-mat.stat-mech Combinatorics math.CO FOS Physical sciences FOS Mathematics |
description |
We study the T-system of type $A_\infty$, also known as the octahedron recurrence/equation, viewed as a 2+1-dimensional discrete evolution equation. Generalizing the study of [P. Di Francesco and R. Soto-Garrido. Arctic curves of the octahedron equation. J. Phys. A, 47(28):285204, 34, 2014], we consider initial data along parallel ``slanted" planes perpendicular to an arbitrary admissible direction $(r,s,t)\in {\mathbb Z}_+^3$. The solution of the T-system is interpreted as the partition function of a dimer model on some suitable ``pinecone" graph introduced in [M. Bousquet-Mélou, J. Propp, and J. West. Perfect matchings for the three-term Gale-Robinson sequences. Electron. J. Combin., 16(1):Research Paper 125, 37, 2009]. The T-system formulation and some exact solutions in uniform or periodic cases allow us to explore the thermodynamic limit of the corresponding dimer models and to derive exact arctic curves separating the various phases of the system. ... : 69 pages, 42 figures ... |
format |
Report |
author |
Di Francesco, Philippe Vu, Hieu Trung |
author_facet |
Di Francesco, Philippe Vu, Hieu Trung |
author_sort |
Di Francesco, Philippe |
title |
Arctic curves of the T-system with Slanted Initial Data ... |
title_short |
Arctic curves of the T-system with Slanted Initial Data ... |
title_full |
Arctic curves of the T-system with Slanted Initial Data ... |
title_fullStr |
Arctic curves of the T-system with Slanted Initial Data ... |
title_full_unstemmed |
Arctic curves of the T-system with Slanted Initial Data ... |
title_sort |
arctic curves of the t-system with slanted initial data ... |
publisher |
arXiv |
publishDate |
2024 |
url |
https://dx.doi.org/10.48550/arxiv.2403.02479 https://arxiv.org/abs/2403.02479 |
long_lat |
ENVELOPE(-57.067,-57.067,-63.500,-63.500) |
geographic |
Arctic Garrido |
geographic_facet |
Arctic Garrido |
genre |
Arctic |
genre_facet |
Arctic |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.2403.02479 |
_version_ |
1809761329973559296 |