Conformal boundary conditions in the critical O(n) model and dilute loop models

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

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
3 Department of Physics and Astronomy [USC, Los Angeles]

We study the conformal boundary conditions of the dilute O(n) model in two dimensions. A pair of mutually dual solutions to the boundary Yang-Baxter equations are found. They describe anisotropic special transitions, and can be interpreted in terms of symmetry breaking interactions in the O(n) model. We identify the corresponding boundary condition changing operators, Virasoro characters, and conformally invariant partition functions. We compute the entropies of the conformal boundary states, and organize the flows between the various boundary critical points in a consistent phase diagram. The operators responsible for the various flows are identified. Finally, we discuss the relation to open boundary conditions in the O(n) model, and present new crossing probabilities for Ising domain walls.

Mots clés: boundary loop model; CFT; Coulomb gas; O(n) model; surface critical behaviour; crossing formula

Domaines: Physique mathématique [math-ph]

Jerome Dubail, Jesper Lykke Jacobsen, Hubert Saleur. Conformal boundary conditions in the critical O(n) model and dilute loop models. 2009. ⟨hal-00382588⟩