A RIGOROUS RENORMALIZATION-GROUP METHOD FOR INTERFACES IN RANDOM-MEDIA

We prove the existence Gibbs states describing rigid interfaces in a d isordered solid-on-solid (SOS) for low temperatures and for weak disor der in dimension D greater-than-or-equal-to 4. This extends earlier re sults for hierarchical models to the more realistic models and proves a long-standing conjecture. The proof is based on the renormalization group method of Bricmont and Kupiainen originally developed for the an alysis of low-temperature phases of the random field Ising model. In a broader context, we generalize this method to a class of systems with non-compact single-site state space.