SELF-AVOIDING WALKS IN 2 TO 5 DIMENSIONS - EXACT ENUMERATIONS AND SERIES STUDY

The method of concatenation (the addition of precomputed shorter chains to the ends of a centrally generated longer chain) has permitted the extension of the exact series for C(N)-the number of distinct configurations for self-avoiding walks of length N. We report on the leading exponent-gamma and x(c) (the reciprocal of the connectivity constant) for the 2D Honeycomb lattice (42 terms) 1.3437, 0.541 1968; the 2D square lattice (30 terms) 1.3436, 0.379 0520; the 3D simple cubic lattice (23 terms) 1.161 932, 0.213 4987; the 4D hypercubic (18 terms) gamma congruent-to 1, 0.147 60 and the 5D hypercubic lattice (13 terms) gamma less-than-or-equal-to 1.025, 0.113 05. In addition we have also evaluated the leading correction terms: honeycomb DELTA congruent-to 1, square DELTA congruent-to 0.85, simple cubic DELTA congruent-to 1.0 and the 4D hypercubic logarithmic correction with delta congruent-to 0.25.