  We study the influence of a correlated disorder on the localization phase
transition in the pinning model. When correlations are strong enough, a strong
disorder regime arises: large and frequent attractive regions appear in the
environment. We present here a pinning model in random binary ({-1,1}-valued)
environment. Defining strong disorder via the requirement that the probability
of the occurrence of a large attractive region is sub-exponential in its size,
we prove that it coincides with the fact that the critical point is equal to
its minimal possible value. We also stress that in the strong disorder regime,
the phase transition is smoother than in the homogeneous case, whatever the
critical exponent of the homogeneous model is: disorder is therefore always
relevant. We illustrate these results with the example of an environment based
on the sign of a Gaussian correlated sequence, in which we show that the phase
transition is of infinite order in presence of strong disorder. Our results
contrast with results known in the literature, in particular in the case of an
IID disorder, where the question of the influence of disorder on the critical
properties is answered via the so-called Harris criterion, and where a
conventional relevance/irrelevance picture holds.
