Arctic curves of the 6V model with partial DWBC and double Aztec rectangles

Jean-Francois de KEMMETER; Bryan DEBIN; Philippe RUELLE

doi:10.1088/1751-8121/ac7c48

Arctic curves of the 6V model with partial DWBC and double Aztec rectangles

Jean-Francois de KEMMETER
, Bryan DEBIN
, Philippe RUELLE

Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

119 Téléchargements (Pure)

Résumé

Previous numerical studies have shown that in the disordered and anti-
ferroelectric phases the six-vertex (6V) model with partial domain wall bound-
ary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown.
The model is defined on a s × n square lattice (s <= n). In this paper, we derive
the analytic expression of the arctic curve, for a = b = 1 and c = √2 (Δ = 0),
while keeping the ratio s/n ∈ [0, 1] as a free parameter. The computation relies
on the tangent method. We also consider domino tilings of double Aztec rectan-
gles 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.

langue originale	Anglais
Numéro d'article	305004
journal	Journal of Physics A: Mathematical and Theoretical
Volume	55
Numéro de publication	30
Les DOIs	https://doi.org/10.1088/1751-8121/ac7c48
Etat de la publication	Publié - 29 juil. 2022

Accès au document

10.1088/1751-8121/ac7c48

6V_and_DoubleAztecRectanglesmanuscrit soumis, 7,84 MB

https://iopscience.iop.org/article/10.1088/1751-8121/ac7c48

Autres fichiers et liens

Lien vers la publication sur Scopus

Processus de réaction-diffusion sur des réseaux temporels et non-normaux
de Kemmeter, J.-F. (Responsable du Projet) & Carletti, T. (Promoteur)
1/10/20 → 30/09/22
Projet: Recherche

Plateforme Technologique Calcul Intensif
Champagne, B. (!!Manager)
Plateforme technologique Calcul intensif
Equipement/installations: Plateforme technolgique

Contient cette citation

@article{0d92a8dd8eaa4db48d363b4c82822a9f,

title = "Arctic curves of the 6V model with partial DWBC and double Aztec rectangles",

abstract = "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 × n square lattice (s ≤ n). In this paper, we derive the analytic expression of the arctic curve, for a = b = 1 and c=2 (Δ= 0), while keeping the ratio s/n ϵ [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.",

keywords = "arctic phenomenon, domino tilings, double Aztec rectangle, integrable lattice model, six-vertex model",

author = "\{de KEMMETER\}, Jean-Francois and Bryan DEBIN and Philippe RUELLE",

note = "Funding Information: BD and JFDK contributed equally to this work. The authors thank Timoteo Carletti and Filippo Colomo for useful discussions. BD acknowledges the financial support of the Fonds Sp{\'e}ciaux de Recherche (FSR) of the Universit{\'e} catholique de Louvain, the Fonds de la Recherche Scientifique (FNRS) and the Fonds Wetenschappelijk Onderzoek—Vlaanderen (FWO) under EOS Project No. 30889451. JFDK is supported by a FNRS Aspirant Fellowship under the Grant FC38477. PR is a Senior Research Associate of FRS-FNRS. Part of the results were obtained using the computational resources provided by the {\textquoteleft}Consortium des Equipements de Calcul Intensif{\textquoteright} (CECI), funded by the Fonds de la Recherche Scientifique de Belgique (FRS-FNRS) under Grant No. 2.5020.11 and by the Walloon Region. Publisher Copyright: {\textcopyright} 2022 IOP Publishing Ltd.",

year = "2022",

month = jul,

day = "29",

doi = "10.1088/1751-8121/ac7c48",

language = "English",

volume = "55",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "30",

}

TY - JOUR

T1 - Arctic curves of the 6V model with partial DWBC and double Aztec rectangles

AU - de KEMMETER, Jean-Francois

AU - DEBIN, Bryan

AU - RUELLE, Philippe

N1 - Funding Information: BD and JFDK contributed equally to this work. The authors thank Timoteo Carletti and Filippo Colomo for useful discussions. BD acknowledges the financial support of the Fonds Spéciaux de Recherche (FSR) of the Université catholique de Louvain, the Fonds de la Recherche Scientifique (FNRS) and the Fonds Wetenschappelijk Onderzoek—Vlaanderen (FWO) under EOS Project No. 30889451. JFDK is supported by a FNRS Aspirant Fellowship under the Grant FC38477. PR is a Senior Research Associate of FRS-FNRS. Part of the results were obtained using the computational resources provided by the ‘Consortium des Equipements de Calcul Intensif’ (CECI), funded by the Fonds de la Recherche Scientifique de Belgique (FRS-FNRS) under Grant No. 2.5020.11 and by the Walloon Region. Publisher Copyright: © 2022 IOP Publishing Ltd.

PY - 2022/7/29

Y1 - 2022/7/29

N2 - 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 × n square lattice (s ≤ n). In this paper, we derive the analytic expression of the arctic curve, for a = b = 1 and c=2 (Δ= 0), while keeping the ratio s/n ϵ [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.

AB - 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 × n square lattice (s ≤ n). In this paper, we derive the analytic expression of the arctic curve, for a = b = 1 and c=2 (Δ= 0), while keeping the ratio s/n ϵ [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.

KW - arctic phenomenon

KW - domino tilings

KW - double Aztec rectangle

KW - integrable lattice model

KW - six-vertex model

UR - https://www.scopus.com/pages/publications/85134852364

U2 - 10.1088/1751-8121/ac7c48

DO - 10.1088/1751-8121/ac7c48

M3 - Article

SN - 1751-8113

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 30

M1 - 305004

ER -

Arctic curves of the 6V model with partial DWBC and double Aztec rectangles

Résumé

Accès au document

Autres fichiers et liens

Empreinte digitale

Projets

Processus de réaction-diffusion sur des réseaux temporels et non-normaux

Équipement

Plateforme Technologique Calcul Intensif

Contient cette citation