Arctic curves of the 20V model on a triangle

• 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

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.