C.: Homogeneous nucleation for Glauber and Kawasaki dynamics in large volumes at low temperatures

In this paper, we study metastability in large volumes at low tempera-tures. We consider both Ising spins subject to Glauber spin-flip dynamics and lattice gas particles subject to Kawasaki hopping dynamics. Let β denote the inverse temperature and let β ⊂ Z2 be a square box with periodic bound-ary conditions such that limβ→ ∞ |β | = ∞. We run the dynamics on β, starting from a random initial configuration where all of the droplets (clus-ters of plus-spins and clusters of particles, respectively) are small. For large β and for interaction parameters that correspond to the metastable regime, we investigate how the transition from the metastable state (with only small droplets) to the stable state (with one or more large droplets) takes place un-der the dynamics. This transition is triggered by the appearance of a sin-gle critical droplet somewhere in β. Using potential-theoretic methods, we compute the average nucleation time (the first time a critical droplet appears and starts growing) up to a multiplicative factor that tends to 1 as β → ∞. It turns out that this time grows as Keβ/|β | for Glauber dynamics and as Kβeβ/|β | for Kawasaki dynamics, where is the local canonical (resp. grand-canonical) energy, to create a critical droplet and K is a constant re-flecting the geometry of the critical droplet, provided these times tend to in-finity (which puts a growth restriction on |β |). The fact that the average nucleation time is inversely proportional to |β | is referred to as homoge-neous nucleation because it says that the critical droplet for the transition appears essentially independently in small boxes that partition β. 1. Introduction an