MSI Weekly Bulletin - Week starting Monday 29 June, 2009

Markov-chain Monte Carlo algorithms provide an important class of tools in statistical mechanics, however they typically suffer from severe critical slowing-down: the autocorrelation times diverge as a critical point is approached, most often as a power-law. One approach to circumventing this slowing-down in spin models involves replacing the spins by an alternate representation, obtained from the original model by algebraic transformation. The "cluster algorithms", first introduced by Swendsen and Wang in 1987, provide an important example of this approach, and generically involve performing global updates in a clever way. Another more recent example are the so-called "worm algorithms", first discussed by Prokof'ev and Svistunov, which simulate the high-temperature graphs of the spin model, considered as a statistical-mechanical model in their own right. It turns out that, despite the local nature of worm algorithms, they often outperform the competing cluster algorithms. In this talk we will give an introduction to worm algorithms for simulating the Ising model, and go on to discuss a recent combinatorial application involving fully-packed loops.