Estimation of connective constants for two-dimensional lattices from self-avoiding walks in the two-dimensional continuum

摘要

The attrition rate of random walks with excluded volume, [PW --> W'], represents the mean number of "failed" (or "rejected") chains between any two successfully embedded independent configurations W and W'. In this work, we study [PW --> W'] as a function of the number of monomers and the excluded volume interaction for chains in the two-dimensional continuum. Our result can also be applied to lattice models, provided that an "effective" radius of excluded volume is introduced. The relation between the [PW --> W'] values in the continuum and in lattice models leads to a simple analytical approximation for the connective constants of all common two-dimensional lattices. [S1063-651X(98)02211-9]. [References: 21]