A rigorous renormalization group method for interfaces in random media.
- Bovier, Anton
- Külske, Christof
2010 Mathematics Subject Classification
- 60K40 82B44 82C22 60K35
- Disordered systems, interfaces, SOS-model, renormalization group, contour models
We prove the existence Gibbs states describing rigid interfaces in a disordered solid-on-solid (SOS) for low temperatures and for weak disorder in dimension D ≥ 4. This extends earlier results 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 analysis 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.
- Rev. Math. Phys., 6 (1994), pp. 413--496