Ising Model Observables and Non-Backtracking Walks

Abstract

This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph $G$ and the set of non-backtracking walks on $G$. The techniques used also give formulas for spin-spin correlation functions in terms of non-backtracking walks. The main tools used are Viennot's theory of heaps of pieces and turning numbers on surfaces.

33 pages, 11 figures. Typos and errors corrected, exposition improved, results unchanged

References in corpus (3)

• Conformal Invariance of Spin Correlations in the Planar Ising Model
• The signed loop approach to the Ising model: foundations and critical point
• Holomorphic Spinor Observables in the Critical Ising Model

Cited by in corpus (2)

• Revisiting the combinatorics of the 2D Ising model
• Feynman identity for planar graphs