Character decomposition of Potts model partition functions. II. Toroidal geometry

Abstract

We extend our combinatorial approach of decomposing the partition function of the Potts model on finite two-dimensional lattices of size L x N to the case of toroidal boundary conditions. The elementary quantities in this decomposition are characters K\_{l,D} labelled by a number of bridges l=0,1,...,L and an irreducible representation D of the symmetric group S\_l. We develop an operational method of determining the amplitudes of the eigenvalues as well as some of their degeneracies.