Planar dimers and Harnack curves
Planar dimers and Harnack curves
复制标题
平面二聚体和哈纳克曲线
DOI：
10.1215/s0012-7094-06-13134-4
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发表时间：
2003
影响因子：
2.5
通讯作者：
A. Okounkov
中科院分区：
文献类型：
--
作者：
R. Kenyon;A. Okounkov
在本文中，我们研究了二聚体和Harnack曲线发现的数学ph/0311005之间的联系。我们证明，每一个Harnack曲线出现的一些二聚体模型的谱曲线。我们还证明了给定度的Harnack曲线的空间同胚于一个封闭的八分圆，并且变形虫孔的面积和变形虫触角之间的距离给出了这些全局坐标。我们刻画了亏格为零的Harnack曲线作为等径二聚体的谱曲线，也作为其Ronkin函数与给定的边界条件下的体积极小。
In this paper we study the connection between dimers and Harnack curves discovered in math-ph/0311005. We prove that every Harnack curve arises as a spectral curve of some dimer model. We also prove that the space of Harnack curve of given degree is homeomorphic to a closed octant and that the areas of the amoeba holes and the distances between the amoeba tentacles give these global coordinates. We characterize Harnack curves of genus zero as spectral curves of isoradial dimers and also as minimizers of the volume under their Ronkin function with given boundary conditions.