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

TL;DR

This paper introduces a new class of self-avoiding random walk models with multiple site visit weightings and restrictions, studying their behavior on square and cubic lattices with simulations up to 1024 steps.

Contribution

The paper presents a novel model for polymer collapse involving multiple site visit weights and site visit restrictions, analyzed through extensive simulations.

Findings

Collapse transition depends on model details

Simulation results show sensitivity to restrictions

Evidence of complex behavior in weighted self-avoiding walks

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 $l\geq K$. 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.