Journal of Statistical Physics

, Volume 146, Issue 6, pp 1288–1302 | Cite as

On the Potts Model Partition Function in an External Field

Article

Abstract

We study the partition function of the Potts model in an external (magnetic) field, and its connections with the zero-field Potts model partition function. Using a deletion-contraction formulation for the partition function Z for this model, we show that it can be expanded in terms of the zero-field partition function. We also show that Z can be written as a sum over the spanning trees, and the spanning forests, of a graph G. Our results extend to Z the well-known spanning tree expansion for the zero-field partition function that arises though its connections with the Tutte polynomial.

Keywords

Tutte polynomial Potts model Spanning trees V-polynomial External field Hamiltonian Edge activities Statistical mechanics 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of South AlabamaMobileUSA
  2. 2.Department of MathematicsOregon State UniversityCorvallisUSA

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