Random walks with nearest neighbors prohibited on the diamond lattice

Abstract

Random walks with nearest neighbors prohibited, of lengths N up to 1024 steps, are studied on the three-dimensional diamond lattice. This is a model to describe steric effects given by geometrical constraints on the conformation of macromolecules. Short walks (N⩽20) are exactly enumerated, whereas longer walks are examined by Monte Carlo simulation. A crossover is revealed between two distinct behaviors of the mean values (end-to-end distance and gyration radius), which is due to a short-range influence of the imposed geometrical constraints. The shapes of random walks with nearest neighbors prohibited are also studied. The results are compared to those for self-avoiding random walks on the diamond lattice.