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On the Potts Model Partition Function in an External Field

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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.

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Author notes

  1. Leslie M. McDonald

    Present address: Department of Mathematics, Oregon State University, Corvallis, OR, 97331, USA

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, 36688, USA

    Leslie M. McDonald & Iain Moffatt

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  1. Leslie M. McDonald
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  2. Iain Moffatt
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Correspondence to Iain Moffatt.

Additional information

This work is based on L.M.’s Masters Thesis which was supervised by I.M.

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McDonald, L.M., Moffatt, I. On the Potts Model Partition Function in an External Field. J Stat Phys 146, 1288–1302 (2012). https://doi.org/10.1007/s10955-012-0449-2

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