The arboreal gas and the supersphere sigma model

Jesper Lykke Jacobsen (1, 2) , Hubert Saleur (3, 2)

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
2 SPhT - Service de Physique Théorique
3 Department of Physics and Astronomy [USC, Los Angeles]

We discuss the relationship between the phase diagram of the Q=0 state Potts model, the arboreal gas model, and the supersphere sigma model S^{0,2} = OSP(1/2) / OSP(0/2). We identify the Potts antiferromagnetic critical point with the critical point of the arboreal gas (at negative tree fugacity), and with a critical point of the sigma model. We show that the corresponding conformal theory on the square lattice has a non-linearly realized OSP(2/2) = SL(1/2) symmetry, and involves non-compact degrees of freedom, with a continuous spectrum of critical exponents. The role of global topological properties in the sigma model transition is discussed in terms of a generalized arboreal gas model.

Domaines: Autre [cond-mat.other]; Mécanique statistique [cond-mat.stat-mech]; Physique des Hautes Energies - Théorie [hep-th]

Jesper Lykke Jacobsen, Hubert Saleur. The arboreal gas and the supersphere sigma model. 2005. ⟨hal-00004124⟩