Nucleation barriers, spinodals, and the Ginzburg criterion

Nucleation theory is considered in d-dimensional systems which undergo a nearly mean-field-like transition, such as Ising magnets or mixtures with a large but finite range r of the interaction, or polymer mixtures with chain lengths N₀=N₁=N1. Near two-phase coexistence the nucleation free-energy barriers are F^* r^d (1-T{{T₂}) }^2-d{2} ({{₂₎₄ₗ}) }^- (d-1) and F^* N^ (d{2-1) } (1-T{{T₂}) }^2-d{2} ({{₂₎₄ₗ}) }^- (d-1), respectively, where ₂₎₄ₗ is the order parameter, the deviation of the order parameter in the metastable state from that at coexistence, and T₂ the critical temperatures where the transition is second order. The crossover to nucleation near T₂ where {F^*}{k₁T₂}=c ({{₂₎₄ₗ}) }^- (d-1), c for d2. In the mean-field region, metastable states are well defined up to a narrow region near the spinodal curve ₒ₏ ; the width of this region is given by ({-{ₒ₏) }{₂₎₄ₗ}}^ (3-d{2) }{r^d (1-T{{T₂}) }^2-d{2}}^-1 or {N^ (d{2-1) } (1-T{{T₂}) }^2-d{2}}^-1, respectively. This rounding of the spinodal curve can again be understood by the Ginzburg criterion for the metastable state at near ₒ₏. At the unstable side of the mean-field region, the linear theory of spinodal decomposition holds outside of correspondingly narrow regions close to the spinodal curve, too.