Journal of Statistical Physics

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

On the Potts Model Partition Function in an External Field

  • Leslie M. McDonald
  • Iain Moffatt


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.


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


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© 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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