Scanning method as an unbiased simulation technique and its application to the study of self-attracting random walks

The scanning method proposed by us [J. Phys. A 15, L735 (1982); Macromolecules 18, 563 (1985)] for simulation of polymer chains is further developed and applied, for the first time, to a model with finite interactions. In addition to ‘‘importance sampling,’’ we remove the bias introduced by the scanning method with a procedure suggested recently by Schmidt [Phys. Rev. Lett. 51, 2175 (1983)]; this procedure has the advantage of enabling one to estimate the statistical error. We find these two procedures to be equally efficient. The model studied is an N-step random walk on a lattice, in which a random walk i has a statistical weight &, where p<1 is an attractive energy parameter and $M_i$ is the number of distinct sites visited by walk i.