title: Self-avoiding random walk with multiple site weightings and restrictions.
abstract: 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 omegal 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 omegal=0 for l>or=K. In this Letter 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. We find evidence that the existence of a collapse transition depends sensitively on the details of the model and has an unexpected dependence on dimension.
authors.affiliation: Department of Mathematics and Statistics, The University of Melbourne, 3010, Australia. j.krawczyk@ms.unimelb.edu.au
authors.forename: J
authors.initials: J
authors.lastname: Krawczyk
authors.forename: T
authors.initials: T
authors.lastname: Prellberg
authors.forename: A L
authors.initials: AL
authors.lastname: Owczarek
authors.forename: A
authors.initials: A
authors.lastname: Rechnitzer