On a Type of 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 ${\omega }_l$ 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 ${\omega }_l=0$ for $l\ge K$. 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.

References in corpus (2)

• Phase Transitions of Single Semi-stiff Polymer Chains
• Exact Enumeration Study of Free Energies of Interacting Polygons and Walks in Two Dimensions

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• Semianalytical solutions of Ising-like and Potts-like magnetic polymers on the Bethe lattice