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Title: 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:
 [1]
  1. 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}
}