Event-chain paradigm for Monte Carlo methods: Infinitesimal, irreversible and rejection-free Markov chains.
Manon Michel (LPS-ENS)
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. I explain how a consistent interpretation of the mathematical lifting concept and the factorized Metropolis filter yield a new paradigm of irreversible algorithms. This new class of rejection-free algorithms indeed break detailed balance yet fulfill the global one and display moves that are infinitesimal, instead of finite random local moves.
As an application, I exhibit how event-chain algorithms bring considerable speed-ups for general particles systems, but also for classical continuous spin model, including the notoriously difficult problem of spin glasses. In particular, recent work on Heisenberg spins system shows a qualitative reduction of the dynamical scaling exponent, leading to an infinite speed-up. The powerful event-chain algorithm is general yet easy to implement. Its infinite number of samples provide direct access to observables that could not be obtained directly and complex interactions can be factorized into simple components.