界面自由能的对数尺度效应：唯象理论和Monte Carlo研究
Logarithmic Finite-Size Effects on Interfacial Free Energies: Phenomenological Theory and Monte Carlo Studies
摘要：
共存相（如~）之间界面自由能的计算饱和蒸汽和液体）的界面的分离仍然是一个具有挑战性的问题，这是由于界面的原子识别的困难，以及由于所有长度尺度上的界面波动。从具有界面的系统相对于相应的单相系统的自由能过剩来估计界面张力的方法不受第一个问题的影响，但仍受后者的影响。考虑$d$ -维系统的界面面积$L^{d-1}$和线性尺寸$L_z$在垂直于界面的方向，有人认为，界面的波动导致对数有限尺寸效应的顺序$\ln (L) / L^{d-1}$和顺序$\ln (L_z)/L ^{d-1}$，除了定期的修正（与领先的顺序$\text{const}/L^{d-1}$）。唯象理论预言对数项的前因子是普适的（但取决于所应用的边界条件和所考虑的统计系综）。这些修正的物理起源是作为一个整体的界面的平移熵，“域呼吸”（耦合的界面波动的散装序参量波动的共存域），和毛细管波。使用一个新的变体的合奏开关方法，界面张力发现从蒙特卡罗模拟的$d=2$和$d=3$伊辛模型和Lennard Jones流体。仿真结果与理论预测完全一致。
英文摘要：
The computation of interfacial free energies between coexisting phases (e.g.~saturated vapor and liquid) by computer simulation methods is still a challenging problem due to the difficulty of an atomistic identification of an interface, and due to interfacial fluctuations on all length scales. The approach to estimate the interfacial tension from the free energy excess of a system with interfaces relative to corresponding single-phase systems does not suffer from the first problem but still suffers from the latter. Considering $d$-dimensional systems with interfacial area $L^{d-1}$ and linear dimension $L_z$ in the direction perpendicular to the interface, it is argued that the interfacial fluctuations cause logarithmic finite-size effects of order $\ln (L) / L^{d-1}$ and order $\ln (L_z)/L ^{d-1}$, in addition to regular corrections (with leading order $\text{const}/L^{d-1}$). A phenomenological theory predicts that the prefactors of the logarithmic terms are universal (but depend on the applied boundary conditions and the considered statistical ensemble). The physical origin of these corrections are the translational entropy of the interface as a whole, "domain breathing" (coupling of interfacial fluctuations to the bulk order parameter fluctuations of the coexisting domains), and capillary waves. Using a new variant of the ensemble switch method, interfacial tensions are found from Monte Carlo simulations of $d=2$ and $d=3$ Ising models and a Lennard Jones fluid. The simulation results are fully consistent with the theoretical predictions.
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