Field Theory of Disordered Elastic Interfaces at 3-Loop Order: The $\beta$-Function

Abstract

We calculate the effective action for disordered elastic manifolds in the ground state (equilibrium) up to 3-loop order. This yields the renormalization-group $\beta$-function to third order in $\epsilon =4-d$, 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.

This is the first part of arXiv:1707.09802v1. The remaining part is in arXiv:1707.09802v2. 47 pages, 67 figures. v2: typos corrected and hyper-ref enabled