A Pfaffian Formula for Monomer-Dimer Partition Functions

被引：8

作者：

Giuliani, Alessandro ^{[1
]}

Jauslin, Ian ^{[2
]}

Lieb, Elliott H. ^{[3
,4
]}

机构：

[1] Univ Roma Tre, Dipartimento Matemat & Fis, L Go SL Murialdo 1, I-00146 Rome, Italy

[2] Univ Roma La Sapienza, Dipartimento Fis, Piazzale Aldo Moro 5, I-00185 Rome, Italy

[3] Princeton Univ, Dept Math, Jadwin Hall, Princeton, NJ 08544 USA

[4] Princeton Univ, Dept Phys, Jadwin Hall, Princeton, NJ 08544 USA

来源：

JOURNAL OF STATISTICAL PHYSICS | 2016年 / 163卷 / 02期

关键词：

Monomer-dimer problem; Pfaffian formula; Boundary monomers; CONFORMAL-INVARIANCE; STATISTICAL-MECHANICS; PLANE;

D O I：

10.1007/s10955-016-1484-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the monomer-dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights, with the restriction that the only non-zero monomer weights are those on the boundary. We prove a Pfaffian formula for the corresponding partition function. As a consequence of this result, multipoint boundary monomer correlation functions at close packing are shown to satisfy fermionic statistics. Our proof is based on the celebrated Kasteleyn theorem, combined with a theorem on Pfaffians proved by one of the authors, and a careful labeling and directing procedure of the vertices and edges of the graph.

引用

页码：211 / 238

页数：28

共 38 条

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