Journal of Statistical Physics, Vol. 78, Nos. 3/4, 1995 Erratum: New Lower Bounds on the Self-Avoiding-Walk Connective Constant 1 Takashi Hara, 2 Gordon Slade, 3 and Alan D. Sokal 4 Received August 30, 1994 Due to a coding error in our calculation of the integral ( 1) ,:,.x Co o, x; = IE ,,.,,~. (2~) ~ 1 - d-t ZJ=, cos k~ (1) the values given in the second column of Table IV contain errors in their final four digits. The correct values are given here in Table I. The error is negligible (< 10 -17) for d~>4. These errors do not affect other numerical values quoted, apart from a change in the final digit of the d= 3, (0, 0) entry of Table II, whose correct value is slightly improved to 3.956776. The integral Co(0, 0; 1/(2d)) is equal to the expected number of returns to the origin of the simple random walk in 7/a. For d= 3, this has been computed exactly in terms of an elliptic integral in ref. 1 and in terms of the gamma function in ref. 2. The latter contains an erroneous numerical prefactor, which when corrected as indicated in ref. 3 yields the exact expression 32- 3F(1) F(5) F(7) \24J J This paper appeared in J. Stat. Phys. 72:479-517 (1993). ' Department of Applied Physics, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152, Japan. E-mail: hara@appana.ap.titech.ac.jp. 3 Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4KI. E-mail: slade@mcmaster.ca. 4 Department of Physics, New York University, New York, New York 10003. E-mail: sokal@acf4.nyu.edu. 1187 0022~.715/95/0200-1187507.50/0 ~1 1995PlenumPublishing Corporation