Arctic Curves of the Reflecting Boundary Six Vertex and of the Twenty Vertex Models

Philippe Di Francesco

doi:10.1088/1751-8121/ac17a6

Arctic Curves of the Reflecting Boundary Six Vertex and of the Twenty Vertex Models

Research output: Contribution to journal › Article › peer-review

Abstract

We apply the tangent method of Colomo and Sportiello to predict the arctic curves of the six vertex model with reflecting (U-turn) boundary and of the related twenty vertex model with suitable domain wall boundary conditions on a quadrangle, both in their disordered phase.

Original language	English (US)
Article number	355201
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	54
Issue number	35
DOIs	https://doi.org/10.1088/1751-8121/ac17a6
State	Published - Sep 2021

Keywords

Arctic phenomenon
Domino tilings
Integrable lattice models
Lattice paths
Six vertex model

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modeling and Simulation
Mathematical Physics
Physics and Astronomy(all)

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10.1088/1751-8121/ac17a6

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title = "Arctic Curves of the Reflecting Boundary Six Vertex and of the Twenty Vertex Models",

abstract = "We apply the tangent method of Colomo and Sportiello to predict the arctic curves of the six vertex model with reflecting (U-turn) boundary and of the related twenty vertex model with suitable domain wall boundary conditions on a quadrangle, both in their disordered phase.",

keywords = "Arctic phenomenon, Domino tilings, Integrable lattice models, Lattice paths, Six vertex model",

author = "{Di Francesco}, Philippe",

note = "Funding Information: We are thankful to GAP Ribeiro for bringing references [PR19a, RK15] to our attention. We acknowledge support from the Morris and Gertrude Fine endowment, the NSF Grant DMS18- 02044, and the NSF RTG Grant DMS19-37241. Publisher Copyright: {\textcopyright} 2021 IOP Publishing Ltd.",

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AU - Di Francesco, Philippe

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N2 - We apply the tangent method of Colomo and Sportiello to predict the arctic curves of the six vertex model with reflecting (U-turn) boundary and of the related twenty vertex model with suitable domain wall boundary conditions on a quadrangle, both in their disordered phase.

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KW - Domino tilings

KW - Integrable lattice models

KW - Lattice paths

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Arctic Curves of the Reflecting Boundary Six Vertex and of the Twenty Vertex Models

Abstract

Keywords

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