On the critical curves of the Pinning and Copolymer models in Correlated Gaussian environment
Abstract
We investigate the disordered copolymer and pinning models, in the case of a correlated Gaussian environment with summable correlations, and when the return distribution of the underlying renewal process has a polynomial tail. As far as the copolymer model is concerned, we prove disorder relevance both in terms of critical points and critical exponents, in the case of nonnegative correlations. When some of the correlations are negative, even the annealed model becomes nontrivial. Moreover, when the return distribution has a finite mean, we are able to compute the weak coupling limit of the critical curves for both models, with no restriction on the correlations other than summability. This generalizes the result of Berger, Caravenna, Poisat, Sun and Zygouras \cite{cf:BCPSZ} to the correlated case. Interestingly, in the copolymer model, the weak coupling limit of the critical curve turns out to be the maximum of two quantities: one generalizing the limit found in the IID case \cite{cf:BCPSZ}, the other one generalizing the socalled Monthus bound.
 Publication:

arXiv eprints
 Pub Date:
 April 2014
 DOI:
 10.48550/arXiv.1404.5939
 arXiv:
 arXiv:1404.5939
 Bibcode:
 2014arXiv1404.5939B
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 82B44;
 82D60;
 60K35
 EPrint:
 35 pages