Arctic curves of the 6V model with partial DWBC and double Aztec rectangles

Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex (6V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a s x n square lattice (s <= n). In this paper, w...

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Bibliographic Details
Published in:Journal of Physics A: Mathematical and Theoretical
Main Authors: de Kemmeter, Jean-François, 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. 2022
Subjects:
integrable lattice model
arctic phenomenon
domino tilings
six- vertex model double Aztec rectangle
six-vertex model
double Aztec rectangle
Arctic
Online Access:http://hdl.handle.net/2078.1/263940
https://doi.org/10.1088/1751-8121/ac7c48
Description
Summary:Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex (6V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a s x n square lattice (s <= n). In this paper, we derive the analytic expression of the arctic curve, for a = b = 1 and c = \sqrt{2} (Delta = 0), while keeping the ratio s/n in [0, 1] as a free parameter. The computation relies on the tangent method. We also consider domino tilings of double Aztec rectangles and show via the tangent method that, for particular parameters, the arctic curve is identical to that of the 6V model with partial DWBC. Our results are confirmed by extensive numerical simulations.

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