晶格规范理论与随机介质Ising模型

Pub Date : 2022-07-06 DOI:10.1007/s11040-022-09430-9

Mikhail Skopenkov

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引用次数: 1

摘要

研究了晶格规范理论的线性化问题。线性化理论近似晶格规范理论的方式与O(n)环模型近似自旋O(n)模型的方式相同。在温和的假设下，我们证明了线性化阿贝尔规范理论中可观测值的期望与随机边权的Ising模型中的期望是一致的。我们发现杨-米尔斯理论与四态波茨模型之间有类似的关系。对于后者，我们引入了一个新的可观测值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Lattice Gauge Theory and a Random-Medium Ising Model

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Lattice Gauge Theory and a Random-Medium Ising Model

We study linearization of lattice gauge theory. Linearized theory approximates lattice gauge theory in the same manner as the loop O(n)-model approximates the spin O(n)-model. Under mild assumptions, we show that the expectation of an observable in linearized Abelian gauge theory coincides with the expectation in the Ising model with random edge-weights. We find a similar relation between Yang-Mills theory and 4-state Potts model. For the latter, we introduce a new observable.

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