Exact enumeration of self-avoiding walks on BCC and FCC lattices

Abstract

Self-avoiding walks on the body-centered-cubic (BCC) and face-centered-cubic (FCC) lattices are enumerated up to lengths 28 and 24, respectively, using the length-doubling method. Analysis of the enumeration results yields values for the exponents γ and ν which are in agreement with, but less accurate than, those obtained earlier from enumeration results on the simple cubic lattice. The non-universal growth constant and amplitudes are accurately determined, yielding for the BCC lattice μ = 6.530 520(20), A = 1.1785(40), and D = 1.0864(50), and for the FCC lattice μ = 10.037 075(20), A = 1.1736(24), and D = 1.0460(50).