Design, analysis and application of Monte Carlo algorithms in statistical mechanics

Monte Carlo methods provide a powerful computational tool with an enormous reange of applications, but when applied in statistical mechanics they typically suffer from servere critical slowing-down, so that their computational efficiency tends rapidly to zero as critical point is approached. We will develop novel Monte Carlo algorithms, to simulate a range of models in statistical mechanics, which have radically reduced critical slowing down, and which even exhibit critical speeding-up; a remarkable phanomenon we discovered in 2007 which demands significant further investigation. In addition to developing vastly more efficient algorithms, we will back them up with rigorous mathematical analysis proving that their results can be trusted.