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

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.

### 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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