  In this paper we study the pinning model with correlated Gaussian disorder.
The presence of correlations makes the annealed model more involved than the
usual homogeneous model, which is fully solvable. We prove however that if the
disorder correlations decay fast enough then the annealed critical behaviour is
the same as the homogeneous one. Our result is sharper if the decay is
exponential. The approach we propose relies on the spectral properties of a
transfer or Ruelle-Perron Frobenius operator related to the model. We use
results on these operators that were obtained in the framework of the
thermodynamic formalism for countable Markov shifts. We also provide
large-temperature asymptotics of the annealed critical curve under weaker
assumptions.
