A Pfaffian formula for the Ising partition function of surface graphs

被引：1

作者：

Pham, Anh Minh ^{[1
]}

机构：

[1] Hanoi Natl Univ Educ, 136 Xuan Thuy Rd, Hanoi, Vietnam

来源：

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | 2020年 / 2020卷 / 08期

关键词：

exact results; Ising model; Pfaffian; STATISTICS; DIMERS; MODEL;

D O I：

10.1088/1742-5468/aba1e4

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We give a Pfaffian formula to compute the partition function of the Ising model on any graphGembedded in a closed, possibly non-orientable surface. This formula can be considered as an extension of the generalised Kac-Ward formula in Cimasoni (2010J. Stat. Mech.P07023) to the case of non-orientable surfaces. By combining the ideas of Loebl-Masbaum (2011Adv. Math.226332-49), Tesler (2000J. Comb. TheoryB78198-231), Cimasoni (2009Lett. Math. Phys.87147-79) (2010J. Stat. Mech.P07023) and Chelkak-Cimasoni-Kassel (2017Ann. Inst. Henri PoincareD4309-85), we give a completely elementary proof of the formula.

引用

页数：29

共 19 条

[1]

Chelkak D, 2017, ANN I H POINCARE D, V4, P309, DOI 10.4171/AIHPD/42

[2] Dimers on surface graphs and spin structures. I [J].

Cimasoni, David ;

Reshetikhin, Nicolai .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 275 (01) :187-208

[3] A generalized Kac-Ward formula [J].

Cimasoni, David .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2010,

[4] Dimers on Graphs in Non-Orientable Surfaces [J].

Cimasoni, David .

LETTERS IN MATHEMATICAL PHYSICS, 2009, 87 (1-2) :149-179

[5]

Dolbilin N.P., 1999, IZV MATH+, V63, P79

[6] STATISTICAL MECHANICS OF DIMERS ON A PLANE LATTICE [J].

FISHER, ME .

PHYSICAL REVIEW, 1961, 124 (06) :1664-&

[7]

Galluccio A., 1999, ELECTRON, V6, pR6

[8] NEW SOLUTION OF THE ISING PROBLEM FOR A RECTANGULAR LATTICE [J].

HURST, CA ;

GREEN, HS .

JOURNAL OF CHEMICAL PHYSICS, 1960, 33 (04) :1059-1062

[9] A COMBINATORIAL SOLUTION OF THE 2-DIMENSIONAL ISING MODEL [J].

KAC, M ;

WARD, JC .

PHYSICAL REVIEW, 1952, 88 (06) :1332-1337

[10] STATISTICS OF DIMERS ON A LATTICE .1. NUMBER OF DIMER ARRANGEMENTS ON A QUADRATIC LATTICE [J].

KASTELEYN, P .

PHYSICA, 1961, 27 (12) :1209-+

← 1 2 →