Irreversible Markov chains by the factorized Metropolis filter : Algorithms and applications in particle systems and spin models
Manon Michel (LPS)

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Monte Carlo methods, by sampling high-dimensional integrals through random walks, have revolutionized the understanding of complex systems. The traditional Metropolis local random walks induce however a high rate of rejections, making any simulations around a phase transition point too expensive, as phenomena of dynamical slowing down greatly impede the thermalization of the system.

This thesis deals with the development and application in statistical physics of a general framework for irreversible and rejection-free Markov-chain Monte Carlo methods, through the implementation of the factorized Metropolis filter and the lifting concept. This new class of rejection-free algorithms indeed breaks detailed balance yet fulfills the global one and displays moves that are infinitesimal, instead of finite random local moves. Clear accelerations of the thermalization time are observed in bidimensional soft-particle systems, bidimensional ferromagnetic XY spin systems and three-dimensional XY spin glasses. Last but not least, an important reduction of the critical slowing down is exhibited in three-dimensional ferromagnetic Heisenberg spin systems. The powerful irreversible factorized Metropolis algorithm is general yet easy to implement. In particular, its infinite number of samples provide direct access to observables that could not be obtained directly and complex interactions can be decomposed into simple components.