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

• Published in: Journal of Physics A: Mathematical and Theoretical
• Main Authors: de Kemmeter, Jean-François, Debin, Bryan, Ruelle, Philippe
• Other Authors: Fonds De La Recherche Scientifique - FNRS, Fonds Wetenschappelijk Onderzoek, Fonds Spéciaux de Recherche
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: IOP Publishing 2022
• Subjects: Arctic
• Online Access: http://dx.doi.org/10.1088/1751-8121/ac7c48; https://iopscience.iop.org/article/10.1088/1751-8121/ac7c48; https://iopscience.iop.org/article/10.1088/1751-8121/ac7c48/pdf

Abstract 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 × n square lattice ( s ⩽ n ). In this paper, we derive the analytic expression of the arctic curve, for a = b = 1 and <?CDATA $c=\sqrt{2}$?> c = 2 (Δ = 0), while keeping the ratio s / n ∈ [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.