自旋网络上的无回溯回路汤和统计力学
Non-backtracking loop soups and statistical mechanics on spin networks
摘要：
本文引入并研究了维数为$d\geq2$且结构为自旋网络的图的边上的马尔可夫场。该领域自然出现的泊松模型（汤）的非回溯循环和行走的特点是由空间马尔可夫属性，使条件的边界集上的边缘占用字段的值，在边界的两侧的循环和弧的分布是相互独立的边缘占用字段。该领域有一个吉布斯分布与哈密顿量的总和的条款，其中只涉及边缘事件在同一个顶点。它的自由能量密度和其他量可以精确计算，并分析其临界行为，在任何尺寸。
英文摘要：
We introduce and study a Markov field on the edges of a graph in dimension $d\geq2$ whose configurations are spin networks. The field arises naturally as the edge-occupation field of a Poissonian model (a soup) of non-backtracking loops and walks characterized by a spatial Markov property such that, conditionally on the value of the edge-occupation field on a boundary set, the distributions of the loops and arcs on either side of the boundary are independent of each other. The field has a Gibbs distribution with a Hamiltonian given by a sum of terms which involve only edges incident on the same vertex. Its free energy density and other quantities can be computed exactly, and their critical behavior analyzed, in any dimension.
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