Exact enumerations of self-avoiding lattice walks with different nearest-neighbor contacts

Abstract

Self-avoiding walks on a lattice with m inner contacts are investigated as a model of a polymer chain in solutions for different solvents. Values of several critical exponents are estimated from the exact enumeration data for up to 22 and 20 steps on the square and tetrahedral lattices, respectively. The values of ν and γ estimated for neighbor-avoiding walks (m=0) are in good agreement with those for self-avoiding walks. However, such agreement is not found in δ, the exponent for the end-distance distribution; it suggests a possibility that δ is ruled out from the hypothesis that self- and neighbor-avoiding walks are in same class of universality in contrast to ν and γ. The limiting value of average m per step q is proposed as a parameter to describe the compactness of self-avoiding lattice walks.