二维的乌伦贝克 - 福特模型：用于液相自由能计算的参考系统
The Uhlenbeck-Ford model in two dimensions: Reference system for fluid-phase free-energy calculations
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中文总结 AI 辅助
研究二维乌伦贝克 - 福特模型作为流体自由能计算参考系统，通过精确计算维里系数、结合模拟数据构建表示，确定相图及适用范围，识别各相，证明其作为参考系统对二维 Lennard - Jones 流体自由能计算的实际适用性。
中文摘要 AI 辅助
我们研究乌伦贝克 - 福特（UF）模型作为二维（2D）流体自由能计算的参考系统。精确计算二维维里系数直至十阶，并结合分子模拟数据构建状态方程和过量亥姆霍兹自由能的高精度数值表示。接着确定模型的相图以建立流体相的热力学稳定性极限，从而确定UF模型作为流体参考系统的适用范围。在此分析过程中，识别出固体、六次近晶相和流体相，并表明对于缩放参数$p\lesssim 70$，流体是唯一与密度无关的热力学稳定相。最后，通过二维 Lennard - Jones 流体自由能的热力学积分计算，证明二维 UF 模型作为参考系统的实际适用性。
英文摘要
We investigate the Uhlenbeck-Ford (UF) model as a reference system for free-energy calculations in two-dimensional (2D) fluids. The 2D virial coefficients are computed exactly up to tenth order and combined with molecular simulation data to construct highly accurate numerical representations of the equation of state and the excess Helmholtz free energy. We then determine the phase diagram of the model in order to establish the thermodynamic stability limits of the fluid phase and thereby identify the range of applicability of the UF model as a fluid reference system. In the course of this analysis, we identify the solid, hexatic, and fluid phases, and show that the fluid remains the only thermodynamically stable phase, independent of density, for scaling parameters up to $p\lesssim 70$. Finally, we demonstrate the practical applicability of the 2D UF model as a reference system through thermodynamic integration calculations of the free energy of a two-dimensional Lennard-Jones fluid.
