Variant of expansion (homotopy parameter expansion) applied to the self-avoiding walk

A new analytic expansion scheme to study the self-avoiding walk and critical phenomena is proposed. The scheme is illustrated by the calculation of the density distribution function of the end-to-end distance of a self-avoiding walk. The new scheme is less systematic but more flexible than the ordinary -expansion method, and can give results with at least the same order of accuracy of the -expansion results. It is possible to apply the new scheme to an analytical study of tricritical-critical crossover behavior.