Character decomposition of Potts model partition functions. I. Cyclic geometry

Details Character decomposition of Potts model partition functions. I. Cyclic geometry Character decomposition of Potts model partition functions. I. Cyclic geometry

2006-05-04

arxiv.org/abs/math-ph/0605016v1

Nuclear Physics B 750 (2006) 250-264

Physics

Mathematical Physics

21 pages, 4 figures

Scientific paper

10.1016/j.nuclphysb.2006.05.028

We study the Potts model (defined geometrically in the cluster picture) on finite two-dimensional lattices of size L x N, with boundary conditions that are free in the L-direction and periodic in the N-direction. The decomposition of the partition function in terms of the characters K\_{1+2l} (with l=0,1,...,L) has previously been studied using various approaches (quantum groups, combinatorics, transfer matrices). We first show that the K\_{1+2l} thus defined actually coincide, and can be written as traces of suitable transfer matrices in the cluster picture. We then proceed to similarly decompose constrained partition functions in which exactly j clusters are non-contractible with respect to the periodic lattice direction, and a partition function with fixed transverse boundary conditions.

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