Abstract
The pivot algorithm is the most efficient known method for sampling polymer configurations for self-avoiding walks and related models. Here we introduce two recent improvements to an efficient binary tree implementation of the pivot algorithm: an extension to an off-lattice model, and a parallel implementation.
Highlights
Self-avoiding walks are non-intersecting paths on lattices such as the two-dimensional square lattice or the three-dimensional simple cubic lattice
We evaluated the mean CPU time per pivot move for a range of polymer lengths, for lattice and off-lattice SAW-tree implementations in two and three dimensions on Dell PowerEdge FC630 machines with Intel Xeon E5-2680 CPUs, and plot the results of these computer experiments in Figs 3 and 4
Schnabel and Janke [9] have very recently implemented a binary tree data structure which is similar to the SAW-tree for the bead-necklace model, as well as a model for which the Lennard-Jones interaction is implemented
Summary
Self-avoiding walks are non-intersecting paths on lattices such as the two-dimensional square lattice or the three-dimensional simple cubic lattice. The pivot algorithm is the most efficient known method for sampling self-avoiding walks of fixed length. Recent improvements to the implementation of the pivot algorithm [3,4,5] have dramatically improved computational efficiency to the point where it is possible to rapidly sample polymer configurations with up to 1 billion monomers [6].
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