材料期刊网

Using Wegner's result relating critical exponents s and v for conductivity and localization length, respectively, via dimensionality d and that for v given by Garcia-Garcia, we derive what we term a semiclassical (Sc) relation for v in terms of s, which is independent of dimensionality. Forming the ratio s/v versus d from the above relations, s/v = 0 at d = 2 is due to a singularity in the sc relation for v. We argue that, in reality, s/v = 0 results from s being zero at d = 2. Finally we conjecture that (i) Wegner's prediction s/v = 1 when d = 3 and (ii) v tends to 1/2 at large s, are both insensitive to interactions. (C) 2011 Elsevier Ltd. All rights reserved.