Finite cluster partition functions for the D-vector model

Systematic methods are developed for calculating the partition functions of star topologies in the D-vector model. A particularly simple technique (ladder transformation) is proposed for topologies containing a 2-cycle (ladder topologies), and these constitute numerically the majority of star topologies. The fewer non-ladder topologies need individual attention and three methods are suggested (i) making a selected bond infinite, (ii) using direct averages, (iii) considering the behaviour as D to infinity . By suitable renormalization of the interaction it is shown that as D to 0 the self-avoiding walk model results.