Berlin 2018 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 66: Poster: Stat. Phys. (Gen., Critical Phen., Biol.)
DY 66.8: Poster
Thursday, March 15, 2018, 15:30–18:00, Poster A
Irreversible Markov chains in spin models: Topological excitations — •Ze Lei1 and Werner Krauth1,2 — 1Ecole Normale Superieure, Paris, France — 2The University of Tokyo, Tokyo, Japan
We analyze the convergence of the irreversible event-chain Monte Carlo algorithm for continuous spin models in the presence of topological excitations.
In the two-dimensional XY model, we show that the local nature of the Markov-chain dynamics leads to slow decay of vortex–antivortex correlations in comparision with the fast decorrelation of spin waves.
We propose an assignment algorithm for pairing vortices and antivortices, and show that the maximum vortex–antivortex distance follows a Fréchet description. The contributions of topological excitations to the equilibrium correlations vary from a dynamical critical exponent z∼ 2 at the critical temperature to z∼ 0 in the limit of zero temperature.
In the harmonic approximation of spin waves for dimensions higher than 2, we confirm the event-chain algorithm’s fast relaxation (corresponding to z=0). Its mixing times however remain much larger than equilibrium correlation times at low temperatures.
We also describe the respective influence of topological monopole–antimonopole excitations and of spin waves on the event-chain dynamics in the three-dimensional Heisenberg model.
We expect that the fast relaxation of phonon modes explains the success of the event-chain algorithm at high densities for particle systems.