Tuning the generalized Hybrid Monte Carlo algorithm

TL;DR

This paper analyzes how tuning the randomness in the generalized Hybrid Monte Carlo algorithm can reduce critical slowing down, with theoretical and numerical comparisons for free field theory and the $O(4)$ spin model.

Contribution

It provides an analytic approach to compute autocorrelation functions and demonstrates how tuning randomness can improve algorithm efficiency.

Findings

Autocorrelation functions can be analytically computed for the algorithm.

Tuning randomness reduces the dynamical critical exponent from 2 to 1 for some operators.

Critical slowing down is mitigated for certain operators through parameter tuning.

Abstract

We discuss the analytic computation of autocorrelation functions for the generalized Hybrid Monte Carlo algorithm applied to free field theory and compare the results with numerical results for the $O(4)$ spin model in two dimensions. We explain how the dynamical critical exponent $z$ for some operators may be reduced from two to one by tuning the amount of randomness introduced by the updating procedure, and why critical slowing down is not a problem for other operators.