Tangent method for the arctic curve arising from freezing boundaries

In the paper Di Francesco and Guitter (2018 J. Phys. A: Math. Theor. 51 355201), the authors study the arctic curve arising in random tilings of some planar domains with an arbitrary distribution of defects on one edge. Using the tangent method they derive a parametric equation for portions of arcti...

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Bibliographic Details
Published in:Journal of Statistical Mechanics: Theory and Experiment
Main Authors: Debin, Bryan, Ruelle, Philippe
Other Authors: UCL - SST/IRMP - Institut de recherche en mathématique et physique
Format: Article in Journal/Newspaper
Language:English
Published: Institute of Physics Publishing Ltd. 2019
Subjects:
Solvable lattice models
dimers
rigorous results in statistical mechanics
Arctic
Online Access:http://hdl.handle.net/2078.1/224647
https://doi.org/10.1088/1742-5468/ab4fdd
Description
Summary:In the paper Di Francesco and Guitter (2018 J. Phys. A: Math. Theor. 51 355201), the authors study the arctic curve arising in random tilings of some planar domains with an arbitrary distribution of defects on one edge. Using the tangent method they derive a parametric equation for portions of arctic curve in terms of an arbitrary piecewise differentiable function that describes the defect distribution. When this distribution presents ‘freezing’ intervals, other portions of arctic curve appear and typically have a cusp. These freezing boundaries can be of two types, respectively with maximal or minimal density of defects. Our purpose here is to extend the tangent method derivation of Di Francesco and Guitter (2018 J. Phys. A: Math. Theor. 51 355201) to include these portions, hence answering the open question stated in Di Francesco and Guitter (2018 J. Phys. A: Math. Theor. 51 355201).

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