New Lower Bounds on the Self-Avoiding-Walk Connective Constant

We give an elementary new method for obtaining rigorous lower bounds on the connective constant for self-avoiding walks on the hypercubic lattice Zd. The method is based on loop erasure and restoration, and does not require exact enumeration data. Our bounds are best for high d, and in fact agree with the rst four terms of the 1=d expansion for the connective constant. The bounds are the best to date for dimensions d 3, but do not produce good results in two dimensions. For d = 3; 4; 5; 6, respectively, our lower bound is within 2:4%, 0:43%, 0:12%, 0:044% of the value estimated by series extrapolation.