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

Abstract

We give an elementary new method for obtaining rigorous lower bounds on the connective constant for self-avoiding walks on the hypercubic lattice $Z^d$. 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 $d\ge 3$, 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.

35 pages, 388480 bytes Postscript, NYU-TH-93/02/01

References in corpus (1)

• Algebraic Techniques for Enumerating Self-Avoiding Walks on the Square Lattice

Cited by in corpus (8)

• Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two- and Three-Dimensional Self-Avoiding Walks
• Pathologies of the large-N limit for RP^{N-1}, CP^{N-1}, QP^{N-1} and mixed isovector/isotensor sigma-models
• Scaling of Self-Avoiding Walks in High Dimensions
• The distribution of path lengths of self avoiding walks on Erdős-Rényi networks
• Localization criteria for Anderson models on locally finite graphs
• Matching measure, Benjamini-Schramm convergence and the monomer-dimer free energy
• The distribution of first hitting times of random walks on Erdős-Rényi networks
• Several Constants Arising in Statistical Mechanics