Limiting ring closure probabilities in the self-avoiding walk problem

Concerned with the limiting ring closure probability index ( alpha ). The authors obtain rigorous upper and lower bounds for the numbers of tadpoles weakly embeddable in a lattice. These bounds are used to prove the existence of a particular limit for tadpoles and to derive a lower bound on alpha . Using Monte Carlo methods it is estimated that, for the face-centred cubic lattice, alpha =2.18+or-0.07.