论文标题
重新审视随机平面图上的六列型模型
The six-vertex model on random planar maps revisited
论文作者
论文摘要
我们在一个随机晶格上解决了六个顶点模型，该晶格以组合术语对应于配备了欧拉方向的加权4价平面图的枚举。这个问题完全是，尽管伊万·科斯托夫（Ivan Kostov）在2000年使用矩阵积分技术来解决了这一问题。我们将科斯托夫的工作转换为涉及来自地图的递归分解的功能方程的组合参数，我们使用复杂的分析对其进行了严格的解决。然后，我们研究溶液的模块化特性，在某些特殊情况下，这会导致简化。特别是，在两种特殊情况下，我们重新列出了Bousquet-Mélou和第一作者发现的公式。
We address the six vertex model on a random lattice, which in combinatorial terms corresponds to the enumeration of weighted 4-valent planar maps equipped with an Eulerian orientation. This problem was exactly, albeit non-rigorously solved by Ivan Kostov in 2000 using matrix integral techniques. We convert Kostov's work to a combinatorial argument involving functional equations coming from recursive decompositions of the maps, which we solve rigorously using complex analysis. We then investigate modular properties of the solution, which lead to simplifications in certain special cases. In particular, in two special cases of combinatorial interest we rederive the formulae discovered by Bousquet-Mélou and the first author.
