Comments on the Influence of Disorder for Pinning Model in Correlated Gaussian Environment

Quentin Berger (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study the random pinning model, in the case of a Gaussian environment presenting power-law decaying correlations, of exponent decay a > 0. A similar study was done in a hierachical version of the model [5], and we extend here the results to the non-hierarchical (and more natural) case. We comment on the annealed (i.e. averaged over disorder) model, which is far from being trivial, and we discuss the influence of disorder on the critical properties of the system. We show that the annealed critical exponent ν a is the same as the homogeneous one ν pur , provided that correlations are decaying fast enough (a > 2). If correlations are summable (a > 1), we also show that the disordered phase transition is at least of order 2, showing disorder relevance if ν pur < 2. If correlations are not summable (a < 1), we show that the phase transition disappears.

Mots clés: Pinning Models; Polymer; Disordered systems; Critical Phenomena; Harris criterion; Correlation

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]

Quentin Berger. Comments on the Influence of Disorder for Pinning Model in Correlated Gaussian Environment. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2013, X (2), pp.953-977. ⟨hal-01426319⟩