Arctic curves of the 20V model on a triangle

International audience We apply the Tangent Method of Colomo and Sportiello to predict the arctic curves of the Twenty Vertex model with specific domain wall boundary conditions on a triangle, in the Disordered phase, leading to a phase diagram with six types of frozen phases and one liquid one. The...

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Bibliographic Details
Published in:Journal of Physics A: Mathematical and Theoretical
Main Author: Francesc, Philippe, Di
Other Authors: Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)
Format: Article in Journal/Newspaper
Language:English
Published: HAL CCSD 2023
Subjects:
integrable lattice models
arctic phenomenon
limit shape
ice type models
osculating paths
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Arctic
Online Access:https://hal.science/hal-04216436
https://hal.science/hal-04216436/document
https://hal.science/hal-04216436/file/Di_Francesco_2023_J._Phys._A%20_Math._Theor._56_204001.pdf
https://doi.org/10.1088/1751-8121/acccbe
Description
Summary:International audience We apply the Tangent Method of Colomo and Sportiello to predict the arctic curves of the Twenty Vertex model with specific domain wall boundary conditions on a triangle, in the Disordered phase, leading to a phase diagram with six types of frozen phases and one liquid one. The result relies on a relation to the Six Vertex model with domain wall boundary conditions and suitable weights, as a consequence of integrability. We also perform the exact refined enumeration of configurations.

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