KRAMERS-WANNIER DUALITY AND TUTTE POLYNOMIALS

被引：0

作者：

Kazakov, A. A. ^{[1
,2
,3
,4
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Mech & Math, Moscow, Russia

[2] Demidov Yaroslavl State Univ, Ctr Integrable Syst, Yaroslavl, Russia

[3] Natl Res Univ, Moscow Inst Phys & Technol, Ctr Fundamental Math, Moscow, Moscow, Russia

[4] Kazan Volga Reg Fed Univ, Lobachevsky Inst Math & Mech, Kazan, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2024年 / 220卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

Ising model; Potts model; Tutte polynomials; Biggs model; Kramers-Wannier duality;

D O I：

10.1134/S0040577924080051

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study applications of the connection between the partition functions of the Potts models and Tutte polynomials: it is demonstrated how the Kramers-Wannier duality can be derived from the Tutte duality. Using the "contraction-elimination" relation and the Biggs formalism, we derive the high-temperature expansion and discuss possible methods for generalizing the Kramers-Wannier duality to models on nonplanar graphs.

引用

页码：1304 / 1314

页数：11

共 23 条

[21] A Note on Jacobians, Tutte Polynomials, and Two-Variable Zeta Functions of Graphs
Clancy, Julien
Leake, Timothy
Payne, Sam
EXPERIMENTAL MATHEMATICS, 2015, 24 (01) : 1 - 7
[22] Zero-free regions for multivariate Tutte polynomials (alias Potts-model partition functions) of graphs and matroids
Jackson, Bill
Sokal, Alan D.
JOURNAL OF COMBINATORIAL THEORY SERIES B, 2009, 99 (06) : 869 - 903
[23] Complex zero-free regions at large |q| for multivariate Tutte polynomials (alias Potts-model partition functions) with general complex edge weights
Jackson, Bill
Procacci, Aldo
Sokal, Alan D.
JOURNAL OF COMBINATORIAL THEORY SERIES B, 2013, 103 (01) : 21 - 45

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