Nucleation theory near the classical spinodal

Abstract

We present a field-theoretic description of metastability and nucleation for arbitrary range interaction models near the limit of metastability, i.e., spinodal. We find that as the spinodal is approached, the size of the nucleating droplet diverges in all dimensions. The upper critical dimension is found to be six. For $d<6$, as the spinodal is approached the nucleating droplets become ramified and their free-energy cost goes to zero; thus the system nucleates before reaching the spinodal. The free-energy cost increases rapidly as the range of the interaction, $R$, is increased, so that even for $d<6$ the spinodal can be approached as close as desired by increasing $R$. The internal structure of the ramified droplets in all dimensions is mapped onto that of a percolation cluster. The lifetime, including both the free-energy cost of the nucleating droplet and a dynamic prefactor, diverges in all dimensions; this is due to "critical" slowing down as the spinodal is approached. For $d>6$, the free-energy cost of the ramified droplets diverges as the spinodal is approached; more compact droplets must also be considered. A crossover where the upper critical dimension changes continuously from 6, for spinodal behavior, to 4, for critical-point behavior, is found for the model; this crossover is hypothesized to be absent or unobservable for more realistic models. The initial growth of the droplet is found to take place through compactification rather than through radial accretion as occurs in nucleation near the coexistence curve.