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 first 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, and 6, respectively, our lower bound is within 2.4%, 0.43%, 0.12%, and 0.044% of the value estimated by series extrapolation.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics