On quenched and annealed critical curves of random pinning model with finite range correlations

Abstract

This paper focuses on directed polymers pinned at a disordered and correlated interface. We assume that the disorder sequence is a q-order moving average and show that the critical curve of the annealed model can be expressed in terms of the Perron-Frobenius eigenvalue of an explicit transfer matrix, which generalizes the annealed bound of the critical curve for i.i.d. disorder. We provide explicit values of the annealed critical curve for $q=1$, 2 and a weak disorder asymptotic in the general case. Following the renewal theory approach of pinning, the processes arising in the study of the annealed model are particular Markov renewal processes. We consider the intersection of two replicas of this process to prove a result of disorder irrelevance (i.e. quenched and annealed critical curves as well as exponents coincide) via the method of second moment.

References in corpus (4)

• A replica-coupling approach to disordered pinning models
• Reflection positivity and phase transitions in lattice spin models
• A selection of nonequilibrium issues
• Adjustment coefficient for risk processes in some dependent contexts

Cited by in corpus (5)

• Sharp critical behavior for pinning model in random correlated environment
• Random pinning model with finite range correlations : disorder relevant regime
• The random pinning model with correlated disorder given by a renewal set
• Comments on the Influence of Disorder for Pinning Model in Correlated Gaussian Environment
• Localization of a one-dimensional simple random walk among power-law renewal obstacles