School Seminars and Colloquia

The pivot algorithm for self-avoiding walks


by Nathan Clisby

Institution: The University of Melbourne
Date: Fri 9th May 2008
Time: 3:15 PM
Location: Theatre 1 ICT Building, 111 Barry St, University of Melbourne

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.
Drinks and nibbles will be served at MASCOS, 139 Barry St, after the

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