Département de mathématiques et de statistique, Université de Montréal
The dilute loop models were first introduced by Bernard Nienhuis as an attempt to generalize the O(n) models while preserving integrability. The family of lattice models he constructed was quickly probed numerically and using the Bethe ansatz. It was argued that their continuum limits would be conformal field theories and a conjecture for their central charge was proposed.
Their interest for mathematical physics lie in the fact that observables can be studied with geometric and algebraic tools. Recent results about their geometry (fractal dimensions of their loops) and their algebraic structure (classification of the principal indecomposable modules of the underlying algebra) will be reported.