Electronic Journal of Probability

On the critical curves of the pinning and copolymer models in correlated Gaussian environment

Quentin Berger and Julien Poisat

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We investigate the disordered copolymer and pinning models, in the case of a correlated Gaussian environment with 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 non-negative correlations. When some of the correlations are negative, even the annealed model becomes non-trivial. 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,Caravennale, Poisat, Sun and Zygouras 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, the other one generalizing the so-called Monthus bound.

Article information

Electron. J. Probab., Volume 20 (2015), paper no. 71, 35 pp.

Accepted: 25 June 2015
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
Secondary: 2D60 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Pinning Model Copolymer Model Critical Curve Fractional Moments Coarse Graining Correlations

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Berger, Quentin; Poisat, Julien. On the critical curves of the pinning and copolymer models in correlated Gaussian environment. Electron. J. Probab. 20 (2015), paper no. 71, 35 pp. doi:10.1214/EJP.v20-3514. https://projecteuclid.org/euclid.ejp/1465067177

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