I will discuss phase transitions in simple systems where anyonic quasiparticles can be found: Kitaev’s toric code and the Levin-Wen string-net model. par After a brief review of these exotic excitations in the simplest case of Abelian anyons, I will show that a wide variety of unconventional quantum phase transitions can be found in the presence of a perturbation for the non Abelian case and that the often mentioned robustness of these topological phases is an issue that must be carefully addressed.

LPTMC, Université Paris-6