匹配测度、Benjamini-Schramm收敛与单体-二聚体自由能
Matching measure, Benjamini-Schramm convergence and the monomer-dimer free energy
摘要：
我们定义格L的匹配测度为L中自避游动树的谱测度。我们把这个不变量与收敛到L的有限图序列的单体-二聚体配分函数联系起来。这使得我们可以用测度来表示L的单体-二聚体自由能。利用分析优势的匹配措施的迈耶系列，然后导致新的，严格的界限上的单体二聚体自由能的各种欧几里德晶格。虽然我们的估计只使用以前的论文中给出的计算数据，但它们显着提高了已知的界限。
英文摘要：
We define the matching measure of a lattice L as the spectral measure of the tree of self-avoiding walks in L. We connect this invariant to the monomer-dimer partition function of a sequence of finite graphs converging to L. This allows us to express the monomer-dimer free energy of L in terms of the measure. Exploiting an analytic advantage of the matching measure over the Mayer series then leads to new, rigorous bounds on the monomer-dimer free energies of various Euclidean lattices. While our estimates use only the computational data given in previous papers, they improve the known bounds significantly.
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