SPECTRUM OF SELF-AVOIDING WALK EXPONENTS

A short range interaction is incorporated into the self-avoiding walk (SAW) model of polymer chains by partitioning SAW's into equivalence c lasses of chain configurations having m nearest-neighbor contacts, and performing an energetically weighted averaging over these restricted SAW configurations. Surprisingly, there have been limited studies of t he geometrical properties of ''contact-constrained'' SAW configuration s, which contrasts with the well studied unrestricted SAW's. According ly, we generate Monte Carlo data for the total number of SAW configura tions C-n,C-m having a fixed number of contacts m for chains of length n on square and cubic lattices. Applications of the standard ratio me thod to the C-n,C-m data shows a unique connectivity constant mu (NAW) , corresponding to neighbor-avoiding walks (m = 0), and a ''spectrum'' of gamma exponents which depend on the contact number m. The asymptot ic scaling of the number of contact-constrained SAW's is found to be s imilar to the number of lattice animals and random plaquette surfaces having a fixed cyclomatic index c and genus g, respectively. The exist ence of this common structure is promising for the development of an a nalytic theory of interacting polymers and surfaces.