Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles
Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex ($6$V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a $s\times n$ square lattice ($s\leq n$). In this...
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ftdatacite:10.48550/arxiv.2203.08506 2023-05-15T14:39:31+02:00 Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles de Kemmeter, Jean-François Debin, Bryan Ruelle, Philippe 2022 https://dx.doi.org/10.48550/arxiv.2203.08506 https://arxiv.org/abs/2203.08506 unknown arXiv Creative Commons Attribution Share Alike 4.0 International https://creativecommons.org/licenses/by-sa/4.0/legalcode cc-by-sa-4.0 CC-BY-SA Statistical Mechanics cond-mat.stat-mech Mathematical Physics math-ph Combinatorics math.CO FOS Physical sciences FOS Mathematics Preprint Article article CreativeWork 2022 ftdatacite https://doi.org/10.48550/arxiv.2203.08506 2022-04-01T15:53:32Z Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex ($6$V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a $s\times n$ square lattice ($s\leq n$). In this paper, we derive the analytic expression of the arctic curve, for $a=b=1$ and $c=\sqrt{2}$ ($Δ=0$), while keeping the ratio $s/n \,\in [0,1]$ as a free parameter. The computation relies on the tangent method. We also consider domino tilings of double Aztec rectangles and show via the tangent method that, for particular parameters, the arctic curve is identical to that of the $6$V model with partial DWBC. Our results are confirmed by extensive numerical simulations. : 42 pages, 18 figures Report Arctic DataCite Metadata Store (German National Library of Science and Technology) Arctic |
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Open Polar |
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DataCite Metadata Store (German National Library of Science and Technology) |
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language |
unknown |
topic |
Statistical Mechanics cond-mat.stat-mech Mathematical Physics math-ph Combinatorics math.CO FOS Physical sciences FOS Mathematics |
spellingShingle |
Statistical Mechanics cond-mat.stat-mech Mathematical Physics math-ph Combinatorics math.CO FOS Physical sciences FOS Mathematics de Kemmeter, Jean-François Debin, Bryan Ruelle, Philippe Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles |
topic_facet |
Statistical Mechanics cond-mat.stat-mech Mathematical Physics math-ph Combinatorics math.CO FOS Physical sciences FOS Mathematics |
description |
Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex ($6$V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a $s\times n$ square lattice ($s\leq n$). In this paper, we derive the analytic expression of the arctic curve, for $a=b=1$ and $c=\sqrt{2}$ ($Δ=0$), while keeping the ratio $s/n \,\in [0,1]$ as a free parameter. The computation relies on the tangent method. We also consider domino tilings of double Aztec rectangles and show via the tangent method that, for particular parameters, the arctic curve is identical to that of the $6$V model with partial DWBC. Our results are confirmed by extensive numerical simulations. : 42 pages, 18 figures |
format |
Report |
author |
de Kemmeter, Jean-François Debin, Bryan Ruelle, Philippe |
author_facet |
de Kemmeter, Jean-François Debin, Bryan Ruelle, Philippe |
author_sort |
de Kemmeter, Jean-François |
title |
Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles |
title_short |
Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles |
title_full |
Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles |
title_fullStr |
Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles |
title_full_unstemmed |
Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles |
title_sort |
arctic curves of the $6$v model with partial dwbc and double aztec rectangles |
publisher |
arXiv |
publishDate |
2022 |
url |
https://dx.doi.org/10.48550/arxiv.2203.08506 https://arxiv.org/abs/2203.08506 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_rights |
Creative Commons Attribution Share Alike 4.0 International https://creativecommons.org/licenses/by-sa/4.0/legalcode cc-by-sa-4.0 |
op_rightsnorm |
CC-BY-SA |
op_doi |
https://doi.org/10.48550/arxiv.2203.08506 |
_version_ |
1766311507076841472 |