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

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

Jean-Francois Richard, Jesper Lykke Jacobsen. Character decomposition of Potts model partition functions. I. Cyclic geometry. Nuclear Physics B, 2006, 750, pp.250-264. ⟨10.1016/j.nuclphysb.2006.05.028⟩. ⟨hal-00023818⟩