ON THE STATISTICAL-MECHANICS OF NON-CROSSING CHAINS .3.

I have shown in a previous paper that the generating function for self-avoiding walks with end-to-end displacement specified can be converted into a Mayer-like cluster series by simply taking the reciprocal of the generating function. In a previous letter the results of doing this for the plane square lattice were reported for terms up to z16. The cluster series terms are much less numerous and numerically much smaller than those of the 'raw' self-avoiding walk series and point to the existence of a set of rapidly converging successive approximations for such problems. Guttman's conclusion that the singularity of the self-avoiding walk series may be a confluent one received support. We now report the results of extending the work on the plane square lattice up to z25 and the results of similar work on the simple cubic lattice up to z15 and discuss them briefly. Conclusions from the earlier work are confirmed.