  We study the critical behavior of surface-interacting self-avoiding random
walks on a class of truncated simplex lattices, which can be labeled by an
integer $n\ge 3$. Using the exact renormalization group method we have been
able to obtain the exact values of various critical exponents for all values of
n up to n=6. We also derived simple formulas which describe the asymptotic
behavior of these exponents in the limit of large n ($n\to\infty$). In spite of
the fact that the coordination number of the lattice tends to infinity in this
limit, we found that the most of the studied critical exponents approach
certain finite values, which differ from corresponding values for simple random
walks (without self-avoiding walk constraint).

Statistical Mechanics