  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.
