Percolation, Droplet Models, and Spinodal Points

Abstract

A modified droplet model is proposed that incorporates both compact fluctuations that give rise to weak singularities at the first-order transition, and ramified fluctuations that give rise to spinodals in high dimensions. Renormalization-group considerations and studies of the percolation problem allow the use of ramified fluctuations to calculate spinodal exponents for $d>8$. The problem in lower dimensions is also discussed together with possible interpretation of these exponents in light of the indeterminacy in locating spinodal points.