A density functional for the lattice gas with next-neighbor attractions (Ising model) from fundamental measure theory is applied to the problem of droplet states in three-dimensional, finite systems. The density functional is constructed via an auxiliary model with hard lattice gas particles and lattice polymers to incorporate the attractions. Similar to previous simulation studies, the sequence of droplets changing to cylinders and to planar slabs is found upon increasing the average density $\overline{\rho }$ in the system. Owing to the discreteness of the lattice, additional effects in the state curve for the chemical potential $\mu \left(\overline{\rho }\right)$ are seen upon lowering the temperature away from the critical temperature [oscillations in $\mu \left(\overline{\rho }\right)$ in the slab portion and spiky undulations in $\mu \left(\overline{\rho }\right)$ in the cylinder portion as well as an undulatory behavior of the radius of the surface of tension $R_{\mathrm{s}}$ in the droplet region]. This behavior in the cylinder and droplet region is related to washed-out layering transitions at the surface of liquid cylinders and droplets. The analysis of the large-radius behavior of the surface tension $\gamma \left(R_{\mathrm{s}}\right)$ gave a dominant contribution $\propto 1/{R_{\mathrm{s}}}^2$, although the consistency of $\gamma \left(R_{\mathrm{s}}\right)$ with the asymptotic behavior of the radius-dependent Tolman length seems to suggest a weak logarithmic contribution $\propto ln{R}_{\mathrm{s}}/{R_{\mathrm{s}}}^2$ in $\gamma \left(R_{\mathrm{s}}\right)$. The coefficient of this logarithmic term is smaller than a universal value derived with field-theoretic methods.

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基于密度泛函理论的晶格气体中的液滴凝聚

将来自基本测度理论的具有下邻吸引力的晶格气体的密度泛函（Ising 模型）应用于三维有限系统中的液滴状态问题。密度泛函是通过一个带有硬晶格气体粒子和晶格聚合物的辅助模型来构建的，以结合吸引力。与之前的模拟研究类似，随着平均密度的增加，发现液滴变成圆柱体和平面板的顺序$\overline{\rho }$在系统中。由于晶格的离散性，化学势状态曲线中的附加效应$\mu \left(\overline{\rho }\right)$ 在将温度降低到远离临界温度时可以看到 [振荡 $\mu \left(\overline{\rho }\right)$ 在平板部分和尖峰起伏 $\mu \left(\overline{\rho }\right)$ 在圆柱部分以及张力表面半径的波动行为 ${\mathrm{电阻}}_{\mathrm{秒}}$在液滴区域]。圆柱体和液滴区域的这种行为与液体圆柱体和液滴表面的层状过渡有关。表面张力大半径行为分析$\gamma \left({\mathrm{电阻}}_{\mathrm{秒}}\right)$ 做出了显着贡献 $\propto 1/{{\mathrm{电阻}}_{\mathrm{秒}}}^2$，虽然一致性 $\gamma \left({\mathrm{电阻}}_{\mathrm{秒}}\right)$ 与半径相关的托尔曼长度的渐近行为似乎表明对数贡献较弱 $\propto 输入{\mathrm{电阻}}_{\mathrm{秒}}/{{\mathrm{电阻}}_{\mathrm{秒}}}^2$ 在 $\gamma \left({\mathrm{电阻}}_{\mathrm{秒}}\right)$. 该对数项的系数小于使用场论方法得出的通用值。