Abstract
Renormalization, which goes back to Wilson's work, consists in searching for a fixed point described by a small number of parameters (the coupling constants). This is only possible in the context of a development in the vicinity of the upper critical dimension. Outside this case, the number of coupling constants usually proliferates under the effect of renormalization, making it impossible to determine fixed points and critical exponents. Functional renormalization involves writing an exact renormalization equation for an infinite number of parameters, i.e. for a function. Trapped interface models can be used to study a number of different problems, such as domain walls in the presence of impurities, vortex lines or crystals in the presence of impurities. After presenting the Larkin model, which predicts both the upper critical dimension and the exponents, Pierre Le Doussal showed how to use the functional renormalization group combined with the method of replicas in the case of trapped interfaces.
