Eigenvalue amplitudes of the Potts model on a torus

We consider the Q-state Potts model in the random-cluster formulation, defined on finite two-dimensional lattices of size L × N with toroidal boundary conditions. Due to the non-locality of the clusters, the partition function Z(L,N) cannot be written simply as a trace of the transfer matrix TL. Using a combinatorial method, we establish the decomposition Z(L,N) = P l,Dk b (l,Dk) Kl,Dk , where the characters Kl,Dk = P i (�i) N are simple traces. In this decomposition, the am′ ) ′ ) , � � ,