Arctic curves of the 20V model on a triangle

Philippe Di Francesco

doi:10.1088/1751-8121/acccbe

Arctic curves of the 20V model on a triangle

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Abstract

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.

Original language	English (US)
Article number	204001
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	56
Issue number	20
DOIs	https://doi.org/10.1088/1751-8121/acccbe
State	Published - May 19 2023

Keywords

arctic phenomenon
ice type models
integrable lattice models
limit shape
osculating paths

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modeling and Simulation
Mathematical Physics
General Physics and Astronomy

Online availability

10.1088/1751-8121/acccbe

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AB - 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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KW - integrable lattice models

KW - limit shape

KW - osculating paths

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ER -

Arctic curves of the 20V model on a triangle

Abstract

Keywords

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