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This paper focuses on directed polymers pinned at a disordered and correlatedinterface. We assume that the disorder sequence is a q-order moving average andshow that the critical curve of the annealed model can be expressed in terms ofthe Perron-Frobenius eigenvalue of an explicit transfer matrix, whichgeneralizes the annealed bound of the critical curve for i.i.d. disorder. Weprovide explicit values of the annealed critical curve for $q=1$, 2 and a weakdisorder asymptotic in the general case. Following the renewal theory approachof pinning, the processes arising in the study of the annealed model areparticular Markov renewal processes. We consider the intersection of tworeplicas of this process to prove a result of disorder irrelevance (i.e.quenched and annealed critical curves as well as exponents coincide) via themethod of second moment.

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