Critical points in coupled Potts models and critical phases in coupled loop models

Paul Fendley (1, 2) , Jesper Lykke Jacobsen (3, 4)

1 Rudolf Peierls Centre for Theoretical Physics
2 Department of Physics
3 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
4 SPhT - Service de Physique Théorique

We show how to couple two critical Q-state Potts models to yield a new self-dual critical point. We also present strong evidence of a dense critical phase near this critical point when the Potts models are defined in their completely packed loop representations. In the continuum limit, the new critical point is described by an SU(2) coset conformal field theory, while in this limit of the the critical phase, the two loop models decouple. Using a combination of exact results and numerics, we also obtain the phase diagram in the presence of vacancies. We generalize these results to coupling two Potts models at different Q.

Mots clés: Potts model; coupled models; loop model; conformal field theory; level-rank duality

Domaines: Mécanique statistique [cond-mat.stat-mech]

Paul Fendley, Jesper Lykke Jacobsen. Critical points in coupled Potts models and critical phases in coupled loop models. 2008. ⟨hal-00264967⟩