Self-avoiding walks on lattices with a long-range-correlated disorder

Abstract

The author considers self-avoiding walks (SAW) on the dilute lattices on which the correlation function of the probability of occupied bonds (sites) obeys a power law r-a for large separation r. The SAW is studied by a renormalisation-group expansion in epsilon =4-d and delta =4-a. The author finds the extended Harris criterion, for n=0 n-vector model or SAW, is that the disorder is irrelevant if av-2>0, which does not depend on the relation between a and d. If the disorder is relevant, the SAW has a new fixed point which has a correlation-length exponent nu =2/a.