标题： 伊辛模型与二维引力的耦合：零亏格分区函数 显示英文标题

标题： The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function

摘要： 我们计算了具有四次相互作用的$2$矩阵模型的$0$亏格自由能，它作为随机$4$正则平面图上伊辛模型配分函数的生成函数。 这与 V.A. Kazakov 和 D.V. Boulatov 对该模型的预测一致，并且随后通过组合方法对该公式的确认也支持这一结果。 我们还提供了自由能的新参数公式，并给出了相空间的特征描述。 我们的分析基于相关双正交多项式的最陡下降黎曼-希尔伯特分析以及相应的等单形$\tau$函数。 分析中的关键部分是对谱曲线的参数化。 该分析为后续对多临界点的研究奠定了基础，我们将在一篇即将发表的文章中进行研究。 显示英文摘要

摘要： We compute the genus $0$ free energy for the $2$-matrix model with quartic interactions, which acts as a generating function for the Ising model's partition function on a random, $4$-regular, planar graph. This is consistent with the predictions of V.A. Kazakov and D.V. Boulatov on this model, as well as subsequent confirmation of this formula using combinatorial methods. We also provide a new parametric formula for the free energy and give a characterization of the phase space. Our analysis is based on a steepest descent Riemann-Hilbert analysis of the associated biorthogonal polynomials and the corresponding isomonodromic $\tau$-function. A key ingredient in the analysis is a parametrization of the spectral curve. This analysis lays the groundwork for the subsequent study of the multicritical point, which we will study in a forthcoming work.