Statistics of self-avoiding walks on randomly diluted lattice

Abstract

A comprehensive numerical study of self-avoiding walks (SAW's) on randomly diluted lattices in two and three dimensions is carried out. The critical exponents $ν$ and $χ$ are calculated for various different occupation probabilities, disorder configuration ensembles, and walk weighting schemes. These results are analyzed and compared with those previously available. Various subtleties in the calculation and definition of these exponents are discussed. Precise numerical values are given for these exponents in most cases, and many new properties are recognized for them.