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

Abstract

Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex ($6$V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a $s\times n$ square lattice ($s\le n$). 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 $6$V model with partial DWBC. Our results are confirmed by extensive numerical simulations.

arXiv comment42 pages, 18 figures

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Cited by in corpus (1)

• Double tangent method for two-periodic Aztec diamonds