English

Ising Model Observables and Non-Backtracking Walks

Combinatorics 2014-10-14 v3 Probability

Abstract

This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph GG and the set of non-backtracking walks on GG. 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.

Keywords

Cite

@article{arxiv.1209.3996,
  title  = {Ising Model Observables and Non-Backtracking Walks},
  author = {Tyler Helmuth},
  journal= {arXiv preprint arXiv:1209.3996},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-21T22:07:22.073Z