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A note on the discrete Gaussian free field with disordered pinning on Zd, d≥2

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  • Coquille, L.
  • Miłoś, P.

Abstract

We study the discrete massless Gaussian free field on Zd, d≥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 R+, is deterministic, and strictly smaller than the annealed free energy whenever the latter is strictly positive.

Suggested Citation

  • Coquille, L. & Miłoś, P., 2013. "A note on the discrete Gaussian free field with disordered pinning on Zd, d≥2," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3542-3559.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:9:p:3542-3559
    DOI: 10.1016/j.spa.2013.04.022
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    References listed on IDEAS

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    1. Külske, Christof & Orlandi, Enza, 2008. "Continuous interfaces with disorder: Even strong pinning is too weak in two dimensions," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1973-1981, November.
    2. Janvresse, É. & de la Rue, T. & Velenik, Y., 2005. "Pinning by a sparse potential," Stochastic Processes and their Applications, Elsevier, vol. 115(8), pages 1323-1331, August.
    3. Caputo, P. & Velenik, Y., 2000. "A note on wetting transition for gradient fields," Stochastic Processes and their Applications, Elsevier, vol. 87(1), pages 107-113, May.
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