The pivot algorithm for self-avoiding walks
by Nathan Clisby
Abstract: The self-avoiding walk (SAW) is an important model in statistical mechanics, as it is a standard model in the study of critical phenomena
(phase transitions) and in addition it accurately characterises the excluded volume effect of real polymers (long chain molecules).
The pivot algorithm is a technique with a long history, and is an extremely powerful tool in the study of SAWs. For a number of important quantities (e.g. critical exponents) it is by far the most efficient known
method of calculation. It works via a Markov chain where successive SAWs
are generated by attempting to 'pivot' part of the walk by rotating or reflecting the walk around a randomly selected pivot point. I will explain how to implement the pivot algorithm and why it is so effective, and then
describe my current research: by incorporating additional geometric
information while running the Markov chain it is possible to dramatically
improve the speed of the algorithm.
***Nathan will repeat his MASCOS seminar (held on the 9th of May) for the Department of Mathematics and Statistics Statistical Mechanics series.
Nathan will add a few extra details to the stat mech talk but the overlap
is so large that he would encourage people to only attend one of the seminars.
For More Information: Contact: Iwan Jensen I.Jensen@ms.unimelb.edu.au