Improved grand canonical sampling of vapour-liquid transitions

Simulation within the grand canonical ensemble is the method of choice for
accurate studies of first order vapour-liquid phase transitions in model
fluids. Such simulations typically employ sampling that is biased with respect
to the overall number density in order to overcome the free energy barrier
associated with mixed phase states. However, at low temperature and for large
system size, this approach suffers a drastic slowing down in sampling
efficiency. The culprits are geometrically induced transitions (stemming from
the periodic boundary conditions) which involve changes in droplet shape from
sphere to cylinder and cylinder to slab. Since the overall number density
doesn't discriminate sufficiently between these shapes, it fails as an order
parameter for biasing through the transitions. Here we report two approaches to
ameliorating these difficulties. The first introduces a droplet shape based
order parameter that generates a transition path from vapour to slab states for
which spherical and cylindrical droplet are suppressed. The second simply
biases with respect to the number density in a tetragonal subvolume of the
system. Compared to the standard approach, both methods offer improved
sampling, allowing estimates of coexistence parameters and vapor-liquid surface
tension for larger system sizes and lower temperatures.