Universality of coupled Potts models

Vladimir S. Dotsenko (1) , Jesper-Lykke Jacobsen (2) , Xuan Son Nguyen (1) , Raoul Santachiara (1)

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

We study systems of M Potts models coupled by their local energy density. Each model is taken to have a distinct number of states, and the permutational symmetry S_M present in the case of identical coupled models is thus broken initially. The duality transformations within the space of 2^M-1 multi-energy couplings are shown to have a particularly simple form. The selfdual manifold has dimension D_M = 2^{M-1}-1. Specialising to the case M=3, we identify a unique non-trivial critical point in the three-dimensional selfdual space. We compare its critical exponents as computed from the perturbative renormalisation group with numerical transfer matrix results. Our main objective is to provide evidence that at the critical point of three different coupled models the symmetry S_3 is restored.

Mots clés: Statistical Mechanics

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

Vladimir S. Dotsenko, Jesper-Lykke Jacobsen, Xuan Son Nguyen, Raoul Santachiara. Universality of coupled Potts models. Nuclear Physics B, 2002, 631, pp.426-446. ⟨hal-00002334⟩