# 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.

- Authors:

- Department of Mathematics, The University of British Columbia, Vancouver, British Columbia V6T 1Z2 (Canada)

- Publication Date:

- OSTI Identifier:
- 22306201

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CORRELATION FUNCTIONS; ISING MODEL; PARTITION FUNCTIONS; QUANTUM MECHANICS; SPIN; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Helmuth, Tyler, E-mail: jhelmt@math.ubc.ca.
```*Ising model observables and non-backtracking walks*. United States: N. p., 2014.
Web. doi:10.1063/1.4881723.

```
Helmuth, Tyler, E-mail: jhelmt@math.ubc.ca.
```*Ising model observables and non-backtracking walks*. United States. doi:10.1063/1.4881723.

```
Helmuth, Tyler, E-mail: jhelmt@math.ubc.ca. Fri .
"Ising model observables and non-backtracking walks". United States.
doi:10.1063/1.4881723.
```

```
@article{osti_22306201,
```

title = {Ising model observables and non-backtracking walks},

author = {Helmuth, Tyler, E-mail: jhelmt@math.ubc.ca},

abstractNote = {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.},

doi = {10.1063/1.4881723},

journal = {Journal of Mathematical Physics},

number = 8,

volume = 55,

place = {United States},

year = {Fri Aug 15 00:00:00 EDT 2014},

month = {Fri Aug 15 00:00:00 EDT 2014}

}

DOI: 10.1063/1.4881723

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