  This is the third in a series of three papers in which we study a
two-dimensional lattice gas consisting of two types of particles subject to
Kawasaki dynamics at low temperature in a large finite box with an open
boundary. Each pair of particles occupying neighboring sites has a negative
binding energy provided their types are different, while each particle has a
positive activation energy that depends on its type. There is no binding energy
between particles of the same type. At the boundary of the box particles are
created and annihilated in a way that represents the presence of an infinite
gas reservoir. We start the dynamics from the empty box and are interested in
the transition time to the full box. This transition is triggered by a critical
droplet appearing somewhere in the box. In the first paper we identified the
parameter range for which the system is metastable, showed that the first
entrance distribution on the set of critical droplets is uniform, computed the
expected transition time up to and including a multiplicative factor of order
one, and proved that the nucleation time divided by its expectation is
exponentially distributed, all in the limit of low temperature. These results
were proved under three hypotheses, and involved three model-dependent
quantities: the energy, the shape and the number of critical droplets. Here
prove the third hypothesis and identify the shape and the number of critical
droplets. The geometric properties of subcritical, critical and supercritical
droplets, which are crucial in determining the metastable behavior of the
system are identified. The geometry turns out to be considerably more complex
than for Kawasaki dynamics with one type of particle, for which an extensive
literature exists. The main motivation behind our work is to understand
metastability of multi-type particle systems.
