Irreversible Markov chains in spin models: Topological excitations

Understand

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 while spin waves decorrelate very quickly.
• Using a Frechet description of the maximum vortex-antivortex distance, we quantify the contributions of topological excitations to the equilibrium correlations, and show that they vary from a dynamical critical exponent z \sim 2 at the critical temperature to z \sim 0 in the limit of zero temperature.
• We confirm the event-chain algorithm's fast relaxation (corresponding to z = 0) of spin waves in the harmonic approximation to the XY model.