Scaling limit of domino tilings on a pentagonal domain ...

We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular non-local correlation function, essentially equivalent to the partition function for the do...

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Bibliographic Details
Main Authors: Colomo, Filippo, Pronko, Andrei G.
Format: Report
Language:unknown
Published: arXiv 2024
Subjects:
Mathematical Physics math-ph
Statistical Mechanics cond-mat.stat-mech
Probability math.PR
FOS Physical sciences
FOS Mathematics
Arctic
Online Access:https://dx.doi.org/10.48550/arxiv.2407.07849
https://arxiv.org/abs/2407.07849
id ftdatacite:10.48550/arxiv.2407.07849
record_format openpolar
spelling ftdatacite:10.48550/arxiv.2407.07849 2024-09-09T19:24:27+00:00 Scaling limit of domino tilings on a pentagonal domain ... Colomo, Filippo Pronko, Andrei G. 2024 https://dx.doi.org/10.48550/arxiv.2407.07849 https://arxiv.org/abs/2407.07849 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 Probability math.PR FOS Physical sciences FOS Mathematics article Article Preprint CreativeWork 2024 ftdatacite https://doi.org/10.48550/arxiv.2407.07849 2024-08-01T10:34:36Z We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular non-local correlation function, essentially equivalent to the partition function for the domino tilings of a pentagon-shaped domain, obtained by cutting away a triangular region from a corner of the initial Aztec diamond. We observe a third-order phase transition when the geometric parameters of the obtained pentagonal domain are tuned to have the fifth side exactly tangent to the arctic ellipse of the corresponding initial model. ... : 16 pages, 5 figures; v2: minor changes, references added ... Report Arctic DataCite Arctic
institution Open Polar
collection DataCite
op_collection_id ftdatacite
language unknown
topic Mathematical Physics math-ph
Statistical Mechanics cond-mat.stat-mech
Probability math.PR
FOS Physical sciences
FOS Mathematics
spellingShingle Mathematical Physics math-ph
Statistical Mechanics cond-mat.stat-mech
Probability math.PR
FOS Physical sciences
FOS Mathematics
Colomo, Filippo
Pronko, Andrei G.
Scaling limit of domino tilings on a pentagonal domain ...
topic_facet Mathematical Physics math-ph
Statistical Mechanics cond-mat.stat-mech
Probability math.PR
FOS Physical sciences
FOS Mathematics
description We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular non-local correlation function, essentially equivalent to the partition function for the domino tilings of a pentagon-shaped domain, obtained by cutting away a triangular region from a corner of the initial Aztec diamond. We observe a third-order phase transition when the geometric parameters of the obtained pentagonal domain are tuned to have the fifth side exactly tangent to the arctic ellipse of the corresponding initial model. ... : 16 pages, 5 figures; v2: minor changes, references added ...
format Report
author Colomo, Filippo
Pronko, Andrei G.
author_facet Colomo, Filippo
Pronko, Andrei G.
author_sort Colomo, Filippo
title Scaling limit of domino tilings on a pentagonal domain ...
title_short Scaling limit of domino tilings on a pentagonal domain ...
title_full Scaling limit of domino tilings on a pentagonal domain ...
title_fullStr Scaling limit of domino tilings on a pentagonal domain ...
title_full_unstemmed Scaling limit of domino tilings on a pentagonal domain ...
title_sort scaling limit of domino tilings on a pentagonal domain ...
publisher arXiv
publishDate 2024
url https://dx.doi.org/10.48550/arxiv.2407.07849
https://arxiv.org/abs/2407.07849
geographic Arctic
geographic_facet Arctic
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.2407.07849
_version_ 1809894341287608320

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