论文标题
$ 6 $ V型号的北极曲线，带有部分DWBC和Double Aztec矩形
Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles
论文作者
论文摘要
先前的数值研究表明，在无序和反铁阶段中，具有部分结构域壁边界条件（DWBC）的六个vertex（$ 6 $ V）模型表现出北极曲线，其确切形状尚不清楚。该模型是在$ s \ times n $ square晶格（$ s \ leq n $）上定义的。在本文中，我们得出了北极曲线的分析表达式，以$ a = b = 1 $和$ c = \ sqrt {2} $（$δ= 0 $），同时将比率$ s/n \，\ in [0,1] $作为免费参数。该计算依赖于切线方法。我们还考虑了双AZTEC矩形的多米诺骨牌瓷砖，并通过切线方法显示，对于特定参数，北极曲线与带有部分DWBC的$ 6 $ V模型相同。我们的结果通过广泛的数值模拟证实。
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 ($s\leq n$). In this paper, we derive the analytic expression of the arctic curve, for $a=b=1$ and $c=\sqrt{2}$ ($Δ=0$), 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.
