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Disorder relevance without Harris Criterion: the case of pinning model with $\gamma$-stable environment
- Publication Year :
- 2016
-
Abstract
- We investigate disorder relevance for the pinning of a renewal whose inter-arrival law has tail exponent $\alpha>0$ when the law of the random environment is in the domain of attraction of a stable law with parameter $\gamma \in (1,2)$. We prove that in this case, the effect of disorder is not decided by the sign of the specific heat exponent as predicted by Harris criterion but that a new criterion emerges to decide disorder relevance. More precisely we show that when $\alpha>1-\gamma^{-1}$ there is a shift of the critical point at every temperature whereas when $\alpha< 1-\gamma^{-1}$, at high temperature the quenched and annealed critical point coincide, and the critical exponents are identical.<br />Comment: 25 Pages
- Subjects :
- Mathematics - Probability
Mathematical Physics
60K35, 60K37, 82B27, 82B44
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1610.06786
- Document Type :
- Working Paper