Arctic curves of the 6V 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 (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 c =√2 (∆ = 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.

Fluctuation of the phase boundary in the six-vertex model with domain wall boundary conditions: a Monte Carlo study

“…In the disorder phase, analogous MC algorithms are nowadays commonly adopted in numerical experiments with the six vertex model [46][47][48][49][50][51]. For earlier numerical approaches to ice models, see [52,53].…”