1107.2363 (Leslie M. McDonald et al.)

On the Potts model partition function in an external field    [PDF]

Leslie M. McDonald, Iain Moffatt

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.

View original: http://arxiv.org/abs/1107.2363