Arctic curves of the 6V model with partial DWBC and double Aztec rectangles
Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex (6V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a s x n square lattice (s <= n). In this paper, w...
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ftunivlouvain:oai:dial.uclouvain.be:boreal:263940 2024-05-12T07:58:07+00:00 Arctic curves of the 6V model with partial DWBC and double Aztec rectangles de Kemmeter, Jean-François Debin, Bryan Ruelle, Philippe UCL - SST/IRMP - Institut de recherche en mathématique et physique 2022 http://hdl.handle.net/2078.1/263940 https://doi.org/10.1088/1751-8121/ac7c48 eng eng Institute of Physics Publishing Ltd. boreal:263940 http://hdl.handle.net/2078.1/263940 doi:10.1088/1751-8121/ac7c48 urn:ISSN:1751-8113 urn:EISSN:1751-8121 info:eu-repo/semantics/openAccess Journal of Physics A: Mathematical and Theoretical, Vol. 55, p. 305004 (2022) integrable lattice model arctic phenomenon domino tilings six- vertex model double Aztec rectangle six-vertex model double Aztec rectangle info:eu-repo/semantics/article 2022 ftunivlouvain https://doi.org/10.1088/1751-8121/ac7c48 2024-04-17T16:33:38Z Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex (6V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a s x n square lattice (s <= n). In this paper, we derive the analytic expression of the arctic curve, for a = b = 1 and c = \sqrt{2} (Delta = 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 6V model with partial DWBC. Our results are confirmed by extensive numerical simulations. Article in Journal/Newspaper Arctic DIAL@UCLouvain (Université catholique de Louvain) Arctic Journal of Physics A: Mathematical and Theoretical 55 30 305004 |
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Open Polar |
collection |
DIAL@UCLouvain (Université catholique de Louvain) |
op_collection_id |
ftunivlouvain |
language |
English |
topic |
integrable lattice model arctic phenomenon domino tilings six- vertex model double Aztec rectangle six-vertex model double Aztec rectangle |
spellingShingle |
integrable lattice model arctic phenomenon domino tilings six- vertex model double Aztec rectangle six-vertex model double Aztec rectangle de Kemmeter, Jean-François Debin, Bryan Ruelle, Philippe Arctic curves of the 6V model with partial DWBC and double Aztec rectangles |
topic_facet |
integrable lattice model arctic phenomenon domino tilings six- vertex model double Aztec rectangle six-vertex model double Aztec rectangle |
description |
Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex (6V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a s x n square lattice (s <= n). In this paper, we derive the analytic expression of the arctic curve, for a = b = 1 and c = \sqrt{2} (Delta = 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 6V model with partial DWBC. Our results are confirmed by extensive numerical simulations. |
author2 |
UCL - SST/IRMP - Institut de recherche en mathématique et physique |
format |
Article in Journal/Newspaper |
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 6V model with partial DWBC and double Aztec rectangles |
title_short |
Arctic curves of the 6V model with partial DWBC and double Aztec rectangles |
title_full |
Arctic curves of the 6V model with partial DWBC and double Aztec rectangles |
title_fullStr |
Arctic curves of the 6V model with partial DWBC and double Aztec rectangles |
title_full_unstemmed |
Arctic curves of the 6V model with partial DWBC and double Aztec rectangles |
title_sort |
arctic curves of the 6v model with partial dwbc and double aztec rectangles |
publisher |
Institute of Physics Publishing Ltd. |
publishDate |
2022 |
url |
http://hdl.handle.net/2078.1/263940 https://doi.org/10.1088/1751-8121/ac7c48 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
Journal of Physics A: Mathematical and Theoretical, Vol. 55, p. 305004 (2022) |
op_relation |
boreal:263940 http://hdl.handle.net/2078.1/263940 doi:10.1088/1751-8121/ac7c48 urn:ISSN:1751-8113 urn:EISSN:1751-8121 |
op_rights |
info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.1088/1751-8121/ac7c48 |
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Journal of Physics A: Mathematical and Theoretical |
container_volume |
55 |
container_issue |
30 |
container_start_page |
305004 |
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1798838463946031104 |