93-286 Hara T., Slade, G.
The Self-Avoiding-Walk and Percolation Critical Points in High Dimensions (531K, PostScript) Nov 5, 93
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Abstract. We prove existence of an asymptotic expansion in the inverse dimension, to all orders, for the connective constant for self-avoiding walks on \$\zd\$. For the critical point, defined to be the reciprocal of the connective constant, the coefficients of the expansion are computed through order \$d^{-6}\$, with a rigorous error bound of order \$d^{-7}\$. Our method for computing terms in the expansion also applies to percolation, and for nearest-neighbour independent Bernoulli bond percolation on \$\zd\$ gives the \$1/d\$-expansion for the critical point through order \$d^{-3}\$, with a rigorous error bound of order \$d^{-4}\$. The method uses the lace expansion. (To potential readers: This is my first trial on Texas archive. Any problems, please notify to hara@ap.titech.ac.jp.)

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