Adaptive tuning of chemical potential

[ffreyer]

In simulations that allow tuning of the chemical potential we are often more interested in a certain filling fraction/particle number than a specific value of the chemical potential. It would be nice to have some adaptive tuning for it.

There is a preprint investigating a tuning of the chemical potential based on compressibility (the derivative d<N>/dµ). This is seems fairly simple to implement (perhaps as an update in MonteCarlo.jl) and successful. Though early adjustments seem to be quite overzealous - maybe applying adjustments to µ more slowly would help with that? https://arxiv.org/abs/2201.01296