Instability of a Hierarchical Wedding Cake in a Random Medium:A Mean Field Result

Abstract

We consider a hierarchical interface model imbedded in a disordered medium in interface dimensions d = 2. We rigorously investigate the renormalization group flow for the stochastic variables describing the disorder in the mean field limit of infinite blocklength at zero temperature. The renormalization of these processes can be described on the level of an infinite vector of covariances. It is shown that, although the strength of the disorder renormalizes to zero, the interface exhibits unbounded fluctuations when the system size goes to infinity