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Giacomin, Giambattista; Toninelli, Fabio; Lacoin, Hubert

Marginal relevance of disorder for pinning models. (English) Zbl 1189.60173

Commun. Pure Appl. Math. 63, No. 2, 233-265 (2010).
The effect of disorder on pinning and wetting models is discussed. Let \(\alpha\) be the return probability exponent. The authors prove disorder relevance both for the general \(\alpha={1\over 2}\) pinning model and for the hierarchical pinning model proposed by Derrida, Hakim, and Nannimenus, in the sense that a shift of the quenched critical point with respect to the annealed one. In both cases the Gaussian disorder used and shown that the shift is at least of order \(\exp(-{1\over \beta^4})\) for \(\beta\) small, if \(\beta^2\) is the disorder variance.
Reviewer: Utkir Rozikov (Tashkent)

Cited in 1 Review
Cited in 48 Documents

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F17 Functional limit theorems; invariance principles

Keywords:

marginal relevance; disorder; pinning model; Harris criterion
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References:

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