Dynamical tuning of the chemical potential to achieve a target particle number in grand canonical Monte Carlo simulations

TL;DR

This paper introduces a dynamic method to tune the chemical potential in grand canonical Monte Carlo simulations, enabling precise control of the target particle number with rapid convergence and minimal impact on measurement accuracy.

Contribution

The paper proposes a novel fictitious dynamics approach for chemical potential tuning that improves convergence speed in grand canonical Monte Carlo simulations.

Findings

Rapid convergence of chemical potential tuning.

Minimal impact of tuning inaccuracy on measurement error.

Effective method across various test cases.

Abstract

We present a method to facilitate Monte Carlo simulations in the grand canonical ensemble given a target mean particle number. The method imposes a fictitious dynamics on the chemical potential, to be run concurrently with the Monte Carlo sampling of the physical system. Corrections to the chemical potential are made according to time-averaged estimates of the mean and variance of the particle number, with the latter being proportional to thermodynamic compressibility. We perform a variety of tests, and in all cases find rapid convergence of the chemical potential -- inexactness of the tuning algorithm contributes only a minor part of the total measurement error for realistic simulations.