A perturbative study of delocalisation transition in one-dimensional models with long-range correlated disorder

Abstract

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.