Real space renormalisation group method for the dilute Gaussian model and its relation to the random walk problems near the percolation threshold

Abstract

An isomorphism between the Gaussian model in the magnetic field and the time-dependent conduction-diffusion problem permits the author to develop a real space renormalisation group method for the diluted version of this model by which all single cluster results of the phenomenological scaling theory of Gefen, Aharony and Alexander (1983) are correctly reproduced. An extension of this model to the case of strong bias then provides some restrictions on the validity of their results. The result for the density of states, which the author reproduces in the form predicted by Alexander and Orbach, (1982) is subject to the same kind of restrictions.