by Dr Tim Garoni
Abstract: The main difficulty in using Markov-chain Monte Carlo methods to study
critical phenomena is that near a critical point the size of the
temporal correlations in the Markov chain diverge, just like every
other quantity of interest. For equilibrium problems we only care
about the stationary distribution, so from a practical point of view,
given two Markov chains with the same stationary distribution, we
prefer the one whose autocorrelations diverge most slowly. In 1987,
Swendsen and Wang invented a ground-breaking new algorithm for
simulating the Potts model, whose autocorrelations are in an entirely
different universality class to naive single spin flip algorithms.
In this talk, I'll try to explain what Swendsen and Wang did, how to
understand it in terms of a coupling of the Potts and random cluster
models (the Edwards-Sokal measure), and then discuss some recent
*Warning: This talk is about algorithms, not physics.
For More Information: contact: Mark Sorrell. email: firstname.lastname@example.org