论文标题
双周期AZTEC钻石的双切线方法
Double tangent method for two-periodic Aztec diamonds
论文作者
论文摘要
我们使用八面体复发，该复发概述了KUO为标准AZTEC钻石发现的二次复发，以便对边界进行单一精制和两层分化的分区函数来计算边界，以用于两期的AZTEC Diamonds。在第一种方法中，几何切线方法允许得出北极曲线的参数形式，从而将固体和液相分开。这是通过使用切线方法的最近重新重新制定和无域扩展的单个分区函数来完成的。在第二部分中，我们使用两条切割的切线方法从边界两置分区函数重新绘制北极曲线，我们会在晶格上精确地计算出北极曲线。该曲线满足已知的8度代数方程，其中切线方法具有明确的参数化。
We use the octahedron recurrence, which generalizes the quadratic recurrence found by Kuo for standard Aztec diamonds, in order to compute boundary one-refined and two-refined partition functions for two-periodic Aztec diamonds. In a first approach, the geometric tangent method allows to derive the parametric form of the arctic curve, separating the solid and liquid phases. This is done by using the recently reformulation of the tangent method and the one-refined partition functions without extension of the domain. In a second part, we use the two-refined tangent method to rederive the arctic curve from the boundary two-refined partition functions, which we compute exactly on the lattice. The curve satisfies the known algebraic equation of degree 8, of which either tangent method gives an explicit parametrization.
