The Tutte-Potts connection in the presence of an external magnetic field

7Citations
Citations of this article
13Readers
Mendeley users who have this article in their library.

Abstract

The classical relationship between the Tutte polynomial of graph theory and the Potts model of statistical mechanics has resulted in valuable interactions between the disciplines. Unfortunately, it does not include the external magnetic fields that appear in most Potts model applications. Here we define the V-polynomial, which lifts the classical relationship between the Tutte polynomial and the zero field Potts model to encompass external magnetic fields. The V-polynomial generalizes Noble and Welshs W-polynomial, which extends the Tutte polynomial by incorporating vertex weights and adapting contraction to accommodate them. We prove that the variable field Potts model partition function (with its many specializations) is an evaluation of the V-polynomial, and hence a polynomial with deletion-contraction reduction and Fortuin-Kasteleyn type representation. This unifies an important segment of Potts model theory and brings previously successful combinatorial machinery, including complexity results, to bear on a wider range of statistical mechanics models. © 2011 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Ellis-Monaghan, J. A., & Moffatt, I. (2011). The Tutte-Potts connection in the presence of an external magnetic field. Advances in Applied Mathematics, 47(4), 772–782. https://doi.org/10.1016/j.aam.2011.02.004

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free