Homogeneous nucleation for two-dimensional Kawasaki dynamics

This is the third in a series of three papers in which we study a lattice gas subject to Kawasaki dynamics at inverse temperature β > 0 in a large finite box Λβ⊂Z2 whose volume depends on β. Each pair of neighbouring particles has a negative binding energy−U<0, while each particle has a positive activation energy Δ > 0. The initial configuration is drawn from the grand-canonical ensemble restricted to the set of configurations where all the droplets are subcritical. Our goal is to describe, in the metastable regime Δ ∈ (U, 2U) and in the limit as β → ∞, how and when the system nucleates, i.e., creates a critical droplet somewhere in Λβ that subsequently grows by absorbing particles from the surrounding gas.