Ising model observables and non-backtracking walks

Journal Article · Fri Aug 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4881723· OSTI ID:22306201

Helmuth, Tyler ^[1]

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

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.

• OSTI ID: 22306201
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

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