On a Type of Self-Avoiding Random Walk with Multiple Site Weightings and Restrictions

الأصل · EN

We introduce a new class of models for polymer collapse, given by random walks on regular lattices which are weighted according to multiple site visits. A Boltzmann weight ωₗ is assigned to each (l+1)-fold visited lattice site, and self-avoidance is incorporated by restricting to a maximal number K of visits to any site via setting ωₗ=0 for l≥ K. In this paper we study this model on the square and simple cubic lattices for the case K=3. Moreover, we consider a variant of this model, in which we forbid immediate self-reversal of the random walk. We perform simulations for random walks up to n=1024 steps using FlatPERM, a flat histogram stochastic growth algorithm. Unexpectedly, we find evidence that the existence of a collapse transition depends sensitively on the details of the model.