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The formation and dissolution of a droplet is an important mechanism relatedto various nucleation phenomena. Here, we address the dropletformation-dissolution transition in a two-dimensional Lennard-Jones gas todemonstrate a consistent finite-size scaling approach from two perspectivesusing orthogonal control parameters. For the canonical ensemble, this meansthat we fix the temperature while varying the density and vice versa. Usingspecialised parallel multicanonical methods for both cases, we confirmanalytical predictions at fixed temperature (rigorously only proven for latticesystems) and corresponding scaling predictions from expansions at fixeddensity. Importantly, our methodological approach provides us with referencequantities from the grand canonical ensemble that enter the analyticalpredictions. Our orthogonal finite-size scaling setup can be exploited fortheoretical and experimental investigations of general nucleation phenomena -if one identifies the corresponding reference ensemble and adapts the theoryaccordingly. In this case, our numerical approach can be readily translated tothe corresponding ensembles and thereby proves very useful for numericalstudies of equilibrium droplet formation, in general.

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