Relations between Potts and RSOS models on a torus

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 relationship between Q-state Potts models and staggered RSOS models of the A_{p-1} type on a torus, with sqrt(Q)=2 cos(pi / p). In general the partition functions of these models differ due to clusters of non-trivial topology. However we find exact identities, valid for any temperature and any finite size of the torus, between various modified partition functions in the two pictures. The field theoretic interpretation of these modified partition function is discussed.

Mots clés: Potts model; RSOS model; Pasquier graph

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

Jean-Francois Richard, Jesper Lykke Jacobsen. Relations between Potts and RSOS models on a torus. Nuclear Physics B, 2005, 731, pp.335-351. ⟨10.1016/j.nuclphysb.2005.09.046⟩. ⟨hal-00007587⟩