CRITICAL-BEHAVIOR OF SELF-AVOIDING WALKS ON PERCOLATION CLUSTERS

Abstract

We study the critical properties of a self-avoiding walk on percolation clusters using exact enumerations, in both d = 2 and d = 3. Calculations of the exponent-chi, which measures free-energy fluctuations, clearly show the existence of two distinct phases, one for strong disorder (at the percolation threshold), the other for weak disorder (above the percolation threshold). The nu exponent is, within numerical accuracy, the same in the two phases. However in d = 3, its value, nu = 0.64 +/- 0.015 is significantly larger than on a pure lattice.