Monte Carlo studies of three-dimensional two-step restricted self-avoiding walks

Two-step restricted walk (TSRW) models are a class of restricted self-avoiding walk (SAW) where, in addition to the self-avoidance constraint, certain restrictions are placed upon each pair of successive steps. In this paper, we explore the relationship between the restrictions and the scaling of the average size of walks in three-dimensional models. We use the Prunedenriched Rosenbluth method algorithm to perform Monte Carlo studies in five representative TSRW models in three dimensions. The results present strong numerical evidence that all non-trivial TSRW models in three dimensions have the same size scaling behaviour as unrestricted SAWs. This is in contrast to two dimensions where several universality classes are accepted to exist. In particular, we find no rule analogous to the ‘spiral’ walk of two dimensions. PACS numbers: 05.50.+q, 05.10.Ln, 05.40.−a