Correlation of a macroscopic dent in a wedge with mixed boundary conditions
Correlation of a macroscopic dent in a wedge with mixed boundary conditions
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楔块中宏观凹痕与混合边界条件的相关性
DOI：
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发表时间：
2019
影响因子：
1.3
通讯作者：
Mihai Ciucu
中科院分区：
文献类型：
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作者：
Mihai Ciucu
作为我们正在进行的关于六边形的菱形瓦片的对称类计数的工作的一部分，我们考虑垂直和水平对称的瓦片的情况。为了处理这一问题，我们需要对Kuo的图形凝聚方法进行推广，该方法在存在自由边界的情况下工作。我们的结果使我们能够准确地计算在混合边界条件下90度楔形宏观凹坑的二聚体海洋中的关联。我们利用前人的结果计算了相应的无边界对称化系统的关联，并证明了它的四次根与90度楔形凹陷的关联具有相同的对数渐近性。这是这类涉及宏观缺陷的第一个结果。这表明，带间隙的二聚体系统与2D静电学之间的联系可能比之前认为的更深。
As part of our ongoing work on the enumeration of symmetry classes of lozenge tilings of hexagons with certain four-lobed structures removed from their center, we consider the case of the tilings which are both vertically and horizontally symmetric. In order to handle this, we need an extension of Kuo's graphical condensation method, which works in the presence of free boundary. Our results allow us to compute exactly the correlation in a sea of dimers of a macroscopic dent in a 90 degree wedge with mixed boundary conditions. We use previous results to compute the correlation of the corresponding symmetrized system with no boundary, and show that its fourth root has the same log-asymptotics as the correlation of the dent in the 90 degree wedge. This is the first result of this kind involving a macroscopic defect. It suggests that the connections between dimer systems with gaps and 2D electrostatics may be deeper that previously thought.