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

Jean-Francois de KEMMETER, Bryan DEBIN, Philippe RUELLE

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Abstract

Previous numerical studies have shown that in the disordered and anti-
ferroelectric phases the six-vertex (6V) model with partial domain wall bound-
ary 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 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 rectan-
gles 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.
Original languageEnglish
JournalJournal of Physics A: Mathematical and Theoretical
Volume55
Issue number305004
Publication statusPublished - 14 Jul 2022

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