Self-avoiding path walks on lattices-a new universality class?

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Abstract
The trails problem (self-avoiding path walks) is reconsidered by the conventional series expansion approach. An exact enumeration on the square, triangular and simple cubic lattices is done by computer up to 18, 12 and 11 steps respectively. The more self-consistent and refined results, between the connective constant and the corresponding critical exponent, indicate the possibility of there being a different universality class from that of the self-avoiding walk. An average approach based on Stolz's theorem is proposed which often appears to be smoother and better than the traditional one.

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