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 $N_A=N_B=N\gg 1$. Near two-phase coexistence the nucleation free-energy barriers are $\Delta F^{*} \propto r^d{(1-\frac{T}{T_c})}^{2-\frac{d}{2}}{\left(\frac{\delta \psi }{{\psi }_{\mathrm{coex}}}\right)}^{-(d-1\mathrm{})\mathrm{}}$ and $\Delta F^{*} \propto N^{(\frac{d}{2}-1)}{(1-\frac{T}{T_c})}^{2-\frac{d}{2}}{\left(\frac{\delta \psi }{{\psi }_{\mathrm{coex}}}\right)}^{-(d-1\mathrm{})\mathrm{}}$, respectively, where ${\psi }_{\mathrm{coex}}$ is the order parameter, $\delta \psi$ the deviation of the order parameter in the metastable state from that at coexistence, and $T_c$ the critical temperatures where the transition is second order. The crossover to nucleation near $T_c$ where $\frac{\Delta F^{*}}{k_B{T}_c}=c{\left(\frac{\delta \psi }{{\psi }_{\mathrm{coex}}}\right)}^{-(d-1\mathrm{})\mathrm{}}$, $c$ for $d<\mathrm{}4\mathrm{}$ being a universal constant, is controlled by the same Ginzburg criterion as for the static critical properties, i.e., crossover occurs at $r^d{(1-\frac{T}{T_c})}^{2-\frac{d}{2}}\approx 1$, $N^{(\frac{d}{2}-1)}{(1-\frac{T}{T_c})}^{2-d}\approx 1$. In polymer mixtures, mean-field-like behavior occurs only for $d>\mathrm{}2\mathrm{}$. In the mean-field region, metastable states are well defined up to a narrow region near the spinodal curve ${\psi }_{\mathrm{sp}}$; the width of this region is given by ${\left[\frac{(\psi -{\psi }_{\mathrm{sp}})}{{\psi }_{\mathrm{coex}}}\right]}^{(3-\frac{d}{2})}\approx {\left[r^d{(1-\frac{T}{T_c})}^{2-\frac{d}{2}}\right]}^{-1\mathrm{}}$ or ${\left[N^{(\frac{d}{2}-1)}{(1-\frac{T}{T_c})}^{2-\frac{d}{2}}\right]}^{-1\mathrm{}}$, respectively. This rounding of the spinodal curve can again be understood by the Ginzburg criterion for the metastable state at $\psi$ near ${\psi }_{\mathrm{sp}}$. 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.

• Received 20 June 1983

DOI:https://doi.org/10.1103/PhysRevA.29.341