Self-interacting walks, random spin systems, and the zero-component limit

Emery's analysis of n-component "spin" systems is extended and simplified for the limits n=0,-2,-4,. Restrictions on the spin-weighting function implied by an interpretation of the n→0 limit as a random system are pointed out. Fully explicit relations are also derived for the interpretation of the n→0 correlation function in terms of self-avoiding and, more generally, weighted self-interacting lattice walks.