Irreversible Markov chains by the factorized Metropolis filter : algorithms and applications in particle systems and spin models

Abstract : 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. The first two chapters present the Markov-chain Monte Carlo method and its different implementations in statistical physics. One of the main limitations of Markov-chain Monte Carlo methods arises around phase transitions, where phenomena of dynamical slowing down greatly impede the thermalization of the system. The third chapter introduces the new class of irreversible factorized Metropolis algorithms. Building on the concept of lifting of Markov chains, the factorized Metropolis filter allows to decompose a multidimensional potential into several unidimensional ones. From there, it is possible to define a rejection-free and completely irreversible Markov-chain Monte Carlo algorithm. The fourth chapter reviews the performance of the irreversible factorized algorithm in a wide variety of systems. Clear accelerations of the thermalization time are observed in bidimensional soft-particle systems, bidimensional ferromagnetic XY spin systems and three-dimensional XY spin glasses. Finally, an important reduction of the critical slowing down is exhibited in three-dimensional ferromagnetic Heisenberg spin systems.
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Manon Michel. Irreversible Markov chains by the factorized Metropolis filter : algorithms and applications in particle systems and spin models. Statistical Mechanics [cond-mat.stat-mech]. PSL Research University, 2016. English. ⟨NNT : 2016PSLEE039⟩. ⟨tel-01394204v2⟩

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