On the Potts model partition function in an external field

Details On the Potts model partition function in an external field On the Potts model partition function in an external field

2011-07-12

arxiv.org/abs/1107.2363v2

J. Stat. Phys. 146 (2012) 1288-1302

Mathematics

Combinatorics

Scientific paper

10.1007/s10955-012-0449-2

We study the partition function of 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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