The region of validity of homogeneous nucleation theory

We examine the region of validity of Langer's picture of homogeneous nuclea tion. Our approach is based on a coarse-grained free energy that incorporat es the effect of fluctuations with momenta above a scale k, The nucleation rate I = A(k)exp(-S-k) is exponentially suppressed by the action S-k of the saddle-point configuration that dominates tunnelling. The factor A(k) incl udes a fluctuation determinant around this saddle point. Both S-k and A(k) depend on the choice of k, but, for 1/k close to the characteristic length scale of the saddle point, this dependence cancels in the expression for th e nucleation rate. For very weak first-order phase transitions or in the vi cinity of the spinodal decomposition line, the pre-exponential factor A(k) compensates the exponential suppression exp(-S-k). In these regions the sta ndard nucleation picture breaks down. We give an approximate expression for A(k) in terms of the saddle-point profile, which can be used for quantitat ive estimates and practical tests of the validity of homogeneous nucleation theory, (C) 1999 Elsevier Science B.V. All rights reserved.