A note on the discrete Gaussian Free Field with disordered pinning on Z^d, d\geq 2

Abstract

We study the discrete massless Gaussian Free Field on ${\mathbb{Z}}^d$, $d\ge 2$, in the presence of a disordered square-well potential supported on a finite strip around zero. The disorder is introduced by reward/penalty interaction coefficients, which are given by i.i.d. random variables. Under minimal assumptions on the law of the environment, we prove that the quenched free energy associated to this model exists in ${\mathbb{R}}^{+}$, is deterministic, and strictly smaller than the annealed free energy whenever the latter is strictly positive.

17 pages

References in corpus (8)

• Smoothing effect of quenched disorder on polymer depinning transitions
• Localization and delocalization of random interfaces
• Marginal relevance of disorder for pinning models
• A replica-coupling approach to disordered pinning models
• Pinning of polymers and interfaces by random potentials
• Nonexistence of random gradient Gibbs measures in continuous interface models in $d=2$
• A note on the discrete Gaussian Free Field with disordered pinning on Z^d, d\geq 2
• A second note on the discrete Gaussian Free Field with disordered pinning on Z^d, d\geq 2

Cited by in corpus (4)

• A note on the discrete Gaussian Free Field with disordered pinning on Z^d, d\geq 2
• Disorder and wetting transition: the pinned harmonic crystal in dimension three or larger
• Pinning and disorder relevance for the lattice Gaussian Free Field II: the two dimensional case
• Solid-On-Solid interfaces with disordered pinning