The Droplet Formation-Dissolution Transition in Different Ensembles: Finite-Size Scaling from Two Perspectives

TL;DR

This paper investigates the droplet formation-dissolution transition in a 2D Lennard-Jones gas using finite-size scaling from two orthogonal control parameters, providing a versatile approach for nucleation phenomena analysis.

Contribution

It introduces a consistent finite-size scaling method from two perspectives and validates analytical predictions using specialized multicanonical simulations.

Findings

Confirmed analytical predictions at fixed temperature

Validated scaling predictions at fixed density

Provided reference quantities from grand canonical ensemble

Abstract

The formation and dissolution of a droplet is an important mechanism related to various nucleation phenomena. Here, we address the droplet formation-dissolution transition in a two-dimensional Lennard-Jones gas to demonstrate a consistent finite-size scaling approach from two perspectives using orthogonal control parameters. For the canonical ensemble, this means that we fix the temperature while varying the density and vice versa. Using specialised parallel multicanonical methods for both cases, we confirm analytical predictions at fixed temperature (rigorously only proven for lattice systems) and corresponding scaling predictions from expansions at fixed density. Importantly, our methodological approach provides us with reference quantities from the grand canonical ensemble that enter the analytical predictions. Our orthogonal finite-size scaling setup can be exploited for theoretical and experimental investigations of general nucleation phenomena - if one identifies the corresponding reference ensemble and adapts the theory accordingly. In this case, our numerical approach can be readily translated to the corresponding ensembles and thereby proves very useful for numerical studies of equilibrium droplet formation, in general.