Potential Renormalization Theory Mapping Interatomic Forces onto Lattice Models

原子扩散和置换合金中的有序-无序相变是非常长时间尺度的现象，远远超出了分子动力学模拟的范围。这种现象可以更有效地处理在格子气体模型。基于非格点体系的配分函数应与格点气体模型的配分函数一致的全新直觉，我们提出了“势重整化理论”，它可以导出相应格点气体模型的相互作用参数。我们将这一理论应用于硅晶体和Cu_xAu_<1-x>2合金。也就是说，我们利用势重整化理论确定了不同温度下的相互作用参数，并利用得到的相互作用参数对晶格气体模型进行了晶格蒙特卡罗模拟。由此得到的硅的热膨胀系数和熔化温度与已有的分子动力学模拟结果吻合得很好。此外，所得到的Cu_xAu合金在不同成分x下的有序-无序相变相图<1-x>与实验相图吻合较好。后一个结果最近发表在J.Crystal Growth上。另一方面，我们将这一理论应用于半柔性聚合物溶液的研究，并揭示了聚合物的刚度依赖于温度。我们在2003年10月8 -13日在横滨举行的ICAM-IUMRS上报告了这一情况。现在非常希望将这种强大的方法应用于许多其他系统。

Atomic diffusion and order-disorder phase transition in substitutional alloys are very long-time-scale phenomena, which are far beyond the limit of applying the molecular dynamics simulations. Such phenomena can be more effectively treated in the lattice-gas models. On a completely new intuition that the partition function of the original off-lattice system should coincide with that of the lattice-gas model, we have proposed "the potential renormalization theory", which can deduce the interaction parameters of the corresponding lattice-gas model. We have applied this theory to the silicon crystal and the Cu_xAu_<1-x> alloy. That is, we have determined the interaction parameters at various temperatures by means of the potential renormalization theory and performed the lattice Monte Carlo simulations of the lattice-gas model with the resulting interaction parameters. Thus obtained thermal expansion coefficients and melting temperature of silicon agree well with the result of the preexisting molecular dynamics simulations. Moreover, the obtained phase diagram related to the order-disorder phase transition of the Cu_xAu<1-x> alloy for various compositions x reproduces well the experimental phase diagram. This latter result has recently published in J.Crystal Growth. On the other hand, we have applied this theory to the investigation of semi-flexible polymer solution and revealed that the stiffness of polymers depends on the temperature. We reported it at the ICAM-IUMRS held in Yokohama on Oct.8-13(2003). It is now highly desirable to apply this powerful method to many other systems.