Affiliation:
1. Leipzig University
2. Bernstein Center for Computational Neuroscience Göttingen
3. Max Planck Institute for Dynamics and Self Organization
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 cluster formation, in
general.
Funder
Bundesministerium für Bildung und Forschung
Deutsche Forschungsgemeinschaft