Partition functions are an important research object in combinatorics and mathematical physics [Barvinok, 2016]. In this work, we consider the partition function of the Ising antiferromagnet on random regular graphs and characterize its limiting distribution in the replica symmetric phase up to the Kesten-Stigum bound. Our proof relies on a careful execution of the method of moments, spatial mixing arguments and small subgraph conditioning.

翻译：分区函数是组合学和数学物理学中的一个重要研究对象[Barvinok,2016年]。在这项工作中,我们考虑Ising 抗发酵磁网在随机常规图形中的分割功能,并描述其限制分布在复制的对称阶段直至 Kesten- Stigum 捆绑。我们的证据依赖于仔细执行时间、空间混合参数和小子节调的方法。