On the critical behaviour of self-avoiding walks. II

Abstract

For the self-avoiding walk problem, the coefficients of the chain generating function and of the generating function for the sum of square end-to-end distances have been extended to 20 terms for the triangular lattice, to 27 terms for the diamond lattice, to 21 terms for the simple cubic lattice and to 16 terms for the BCC lattice. Precise estimates of the critical points are obtained, and for the exponents we find that gamma =1.161+or-0.002 and nu =0.592+or-0.003 encompasses all the three-dimensional lattice data.