Ising Model Observables and Non-Backtracking Walks

TL;DR

This paper establishes a new proof linking the Ising model's partition function to non-backtracking walks, providing formulas for correlations using advanced combinatorial techniques.

Contribution

It introduces an alternative proof connecting the Ising model to non-backtracking walks and derives correlation formulas using Viennot's heap theory and surface turning numbers.

Findings

New proof of the Ising model partition function connection

Formulas for spin-spin correlations in terms of non-backtracking walks

Application of heap theory and surface topology techniques

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.