Topological phase transitions

Topological phase transitions remain a widely unexplored domain mainly due to the lack of theoretical tools to analyze them. Indeed, the absence of local order parameter in topologically ordered systems prevents to use the standard machinery based on Ginzburg-Landau theory of phase transitions. I will present some results obtained in two-dimensional lattice models with Abelian and non-Abelian excitations. In particular, combining various analytical and numerical methods, I will give evidence for a new universality class in the perturbed Levin-Wen model with Fibonacci anyons on the honeycomb lattice.