Testing algorithms for critical slowing down

TL;DR

This paper introduces two modified Hybrid Monte Carlo algorithms aimed at reducing critical slowing down in lattice gauge theory simulations by increasing phase space traversal and decreasing autocorrelation times, with preliminary cost comparisons.

Contribution

The paper proposes and tests two new HMC modifications that improve sampling efficiency near the continuum limit in pure gauge field simulations.

Findings

Both algorithms travel farther in phase space per trajectory.

They reduce autocorrelation times for key observables.

Preliminary cost analysis shows potential efficiency gains.

Abstract

We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard HMC evolution for pure gauge fields, studying the autocorrelation times for various quantities including the topological charge.