各向异性海森堡模型对数配分函数的几何展开
Geometric expansion of the log-partition function of the anisotropic Heisenberg model
摘要：
研究了各向异性海森堡模型的对数配分函数在有界区域中的渐近展开式，当该区域扩张到无穷大时，该配分函数的渐近展开式为：使用Ginibre的各向异性海森堡模型的表示作为一个气体的相互作用的复合泊松过程的轨迹，我们发现所有的非递减项的这种扩展。它们是明确的功能积分。作为主要的技术工具，我们使用的集群扩展方法。
英文摘要：
We study the asymptotic expansion of the log-partition function of the anisotropic Heisenberg model in a bounded domain as this domain is dilated to infinity. Using the Ginibre's representation of the anisotropic Heisenberg model as a gas of interacting trajectories of a compound Poisson process we find all the non-decreasing terms of this expansion. They are given explicitly in terms of functional integrals. As the main technical tool we use the cluster expansion method.
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