Anomalous diffusion in random media of any dimensionality

We show, through physical arguments and a renormalization group analysis, that in the presence of long-range correlated random forces, diffusions is anomalous in any dimension. We obtain in general surdiffusive behaviours, except when the random force is the gradient of a potential. In this last situation, with either short or long-range correlations, a subdiffusive behaviour with a disorder dependent exponent is found in the upper critical case (D = 2 for short-range correlations). This is because the β-function vanishes, which is explicitly proven at all orders of the perturbation theory. Apart from this case, a potential force is expected to lead to logarithmic diffusion (1/f noise), as suggested by simple arguments