Basic HTML version of Foils prepared October 22 1997

Foil 77 New Monte Carlo Algorithms

From GCF Talk U - Lewis/NASA 3/9/92 Mardi Gras Conference on Concurrent Computing in Physical Sciences -- February 18, 1993. by Geoffrey C. Fox
1 The Metropolis Algorithm
  • Major problem in Monte Carlo simulation is critical slowing down. Standard algorithms (e.g. Metropolis) do single site, local updates. Number of iterations needed to change the large-scale structure and produce a new uncorrelated configuration diverges as a power of lattice size at a critical point.
2 Cluster Algorithm
  • New multi-spin, non-local algorithms (Swendsen-Wang, Wolff) rapidly change large-scale structure by identifying clusters of sites to be updated at once, greatly reducing critical slowing down.
  • Currently only applicable to a limited class of models
  • Ongoing research includes
    • Extensions to frustrated spin models (e.g. spin glasses) where critical slowing down is extreme
    • Precise measurements of autocorrelations and dynamic critical exponents to help understand dynamics of new algorithms
    • Application of new algorithms to simulation of spin models, e.g. O(3) model, fully frustrated Ising model
    • Parallel cluster algorithms
  • Simulated Tempering
    • New Method of making small changes in temperature while keeping system in equilibrium. Applications include:
    • Allowing tunneling between states at first order phase transitions (e.g. random field Ising model)
    • Global optimization (a la simulated annealing)
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