Character decomposition of Potts model partition functions, II: Toroidal geometry

We extend our combinatorial approach of decomposing the partition function of the Potts model on finite two-dimensional lattices of size L×NL×N to the case of toroidal boundary conditions. The elementary quantities in this decomposition are characters Kl,DKl,D labeled by a number of bridges l=0,1,…,Ll=0,1,…,L and an irreducible representation D   of the symmetric group SlSl. We develop an operational method of determining the amplitudes of the eigenvalues as well as some of their degeneracies.