Self-avoiding walks in two to five dimensions: exact enumerations and series study

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Abstract
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 CN-the number of distinct configurations for self-avoiding walks of length N. The authors report on the leading exponent y and xc (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) y approximately=1, 0.147 60 and the 5D hypercubic lattice (13 terms) y<or=1.025, 0.113 05. In addition they have also evaluated the leading correction terms: honeycomb Delta approximately=1, square Delta approximately=0.85, simple cubic Delta approximately=1.0 and the 4D hypercubic logarithmic correction with delta approximately=0.25.