  We study the delocalisation transition which takes places in one-dimensional
disordered systems when the random potential exhibits specific long-range
correlations. We consider the case of weak disorder; using a systematic
perturbative approach, we show how the delocalisation transition brings about a
change of the scaling law of the inverse localisation length which ceases to be
a quadratic function of the disorder strength and assumes a quartic form when
the threshold separating the localised phase from the extended one is crossed.

Disordered Systems and Neural Networks