# Using Markov-chain Monte Carlo algorithms to study phase transitions in Statistical Mechanics

#### by Dr Tim Garoni

Institution: Monash University
Date: Tue 23rd August 2011
Time: 12:00 PM
Location: Russell Love Theatre, Richard Berry building

Abstract: Problems in statistical mechanics often take the following form: Given a graph, G, consider a probability distribution defined on a space of "configurations" constructed from G, e.g. the set of all k-vertex colourings. In particular, we are interested in the behaviour of such models as the size (number of vertices) of G tends to infinity, because in this limit the probability distribution on the configurations can display "phase transitions". Since exact solutions of such models are rare, much of our understanding of them relies on numerical methods, such as Markov-chain Monte Carlo. Unfortunately, the non-analyticities that make these phase transitions of significant physical interest also manifest themselves in the size of the autocorrelations of the Markov chains employed in their study, often severely affecting their computational efficiency. In this talk I'll discuss some of the current paradigms used to construct Markov-chain Monte Carlo algorithms which avoid, or at least significantly reduce, these efficiency pitfalls near phase transitions.