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

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Monte Carlo methods provide a powerful computational tool with an enormous range of applications. However when applied in statistical mechanics they typically suffer from severe critical slowing-down, so that their computational efficiency tends rapidly to zero as a critical point is approached. We will develop novel, more efficient Monte Carlo algorithms, to simulate a range of models in statistical mechanics and back this up with rigorous mathematical analysis proving that their results can be trusted.