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

Jean-Francois Richard (1, 2) , Jesper Lykke Jacobsen (1, 3)

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
2 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
3 SPhT - Service de Physique Théorique

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.

Domaines: Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]

Jean-Francois Richard, Jesper Lykke Jacobsen. Character decomposition of Potts model partition functions. II. Toroidal geometry. Nuclear Physics B, 2006, 750, pp.229-249. ⟨10.1016/j.nuclphysb.2006.05.027⟩. ⟨hal-00023819⟩