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

Previous numerical studies have shown that in the disordered and antiferroelectric 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 as x n square lattice (s <= n). In this paper, we derive the analytic expression of the arctic curve, fora = b = 1 and c = root 2 (Delta = 0), while keeping the ratio s/n is an element of [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.

Automated summary

This paper investigates the six-vertex model with partial domain wall boundary conditions and domino tilings of double Aztec rectangles. The analytic expression of the arctic curve is derived and confirmed through extensive numerical simulations.