PIRSA:12120025

Adventures with Monte Carlo Simulations of the Self-Avoiding Walk

Janse van Rensburg, E. (2012). Adventures with Monte Carlo Simulations of the Self-Avoiding Walk. Perimeter Institute. https://pirsa.org/12120025

Janse van Rensburg, Esaias. Adventures with Monte Carlo Simulations of the Self-Avoiding Walk. Perimeter Institute, Dec. 12, 2012, https://pirsa.org/12120025 

          @misc{ pirsa_PIRSA:12120025,
            doi = {10.48660/12120025},
            url = {https://pirsa.org/12120025},
            author = {Janse van Rensburg, Esaias},
            keywords = {},
            language = {en},
            title = {Adventures with Monte Carlo Simulations of the Self-Avoiding Walk},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {dec},
            note = {PIRSA:12120025 see, \url{https://pirsa.org}}
          }

Esaias Janse van Rensburg York University

Talk numberPIRSA:12120025
DOI10.48660/12120025
Collection
Talk Type Scientific Series

Abstract

The Rosenbluth Method is a classical kinetic growth Monte Carlo algorithm for growing a self-avoiding walk by appending steps to its endpoint. This algorithm can be generalised by the implementation of more general elementary moves (for example, BFACF elementary moves) to realise kinetic growth algorithms for lattice polygons.  This generalises the counting principle that underlies the Rosenbluth method and the result is a widely applicable class of algorithms which may be used for microcanonical sampling in discrete models.  In addition to self-avoiding walks, several applications of kinetic growth and canonical Monte Carlo algorithms will be presented, including the sampling of trivial words in abstract groups, as well as knotted lattice polygons and discrete lattice spin systems such as the Potts model.     This is work was done in collaboration with Andrew Rechnitzer of the Mathematics Department at the University of British Columbia.