Field theory of disordered elastic interfaces at 3-loop order: The $\beta$-function
Résumé
We calculate the effective action for disordered elastic manifolds in the ground state (equilibrium) up to 3-loop order. This yields the renormalization-group β -function to third order in ε=4−d , in an expansion in the dimension d around the upper critical dimension d=4 . The calculations are performed using exact RG, and several other techniques, which allow us to resolve consistently the problems associated with the cusp of the renormalized disorder.