Slow Forcing in the Projective Dynamics Method

TL;DR

This paper proves that the projective dynamics Monte Carlo algorithm accurately computes metastable state lifetimes without forcing and demonstrates rapid convergence to this limit under slow forcing, supported by numerical evidence on a 3D Potts model.

Contribution

It provides a rigorous proof of the algorithm's accuracy in zero-forcing conditions and shows numerical results on convergence behavior under slow forcing.

Findings

Exact lifetime calculation in zero-forcing case

Rapid approach to zero-forcing limit with slow forcing

Numerical validation on 3D 3-state Potts model

Abstract

We provide a proof that when there is no forcing the recently introduced projective dynamics Monte Carlo algorithm gives the exact lifetime of the metastable state, within statistical uncertainties. We also show numerical evidence illustrating that for slow forcing the approach to the zero-forcing limit is rather rapid. The model studied numerically is the 3-dimensional 3-state Potts ferromagnet.