Limiting ring closure probability on the square lattice

Abstract

A Monte Carlo technique is described for estimating the number of tadpoles of a given size, which are weakly embeddable in a given lattice. Data are reported for the square lattice for tadpoles with up to twenty edges in the head and up to fifty edges in the tail. These data are combined with good self-avoiding walk extrapolants to yield estimates of the limiting probability (pk) of forming a head with k edges, and it is suggested that pk approximately k- alpha where alpha approximately=2.13.