Stability for a continuous SOSinterface model in a randomly perturbed periodic potential
Abstract
We consider the Gibbsmeasures of continuousvalued height configurations on the $d$dimensional integer lattice in the presence a weakly disordered potential. The potential is composed of Gaussians having random location and random depth; it becomes periodic under shift of the interface perpendicular to the baseplane for zero disorder. We prove that there exist localized interfaces with probability one in dimensions $d\geq 3+1$, in a `lowtemperature' regime. The proof extends the method of continuoustodiscrete single site coarse graining that was previously applied by the author for a doublewell potential to the case of a noncompact image space. This allows to utilize parts of the renormalization group analysis developed for the treatment of a contour representation of a related integervalued SOSmodel in [BoK1]. We show that, for a.e. fixed realization of the disorder, the infinite volume Gibbs measures then have a representation as superpositions of massive Gaussian fields with centerings that are distributed according to the infinite volume Gibbs measures of the disordered integervalued SOSmodel with exponentially decaying interactions.
 Publication:

arXiv eprints
 Pub Date:
 December 1998
 DOI:
 10.48550/arXiv.mathph/9812021
 arXiv:
 arXiv:mathph/9812021
 Bibcode:
 1998math.ph..12021K
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Mathematics  Probability;
 82B44 (Primary) 82B28;
 82B41;
 60K35 (Secondary)