Potential Renormalization Theory Mapping Interatomic Forces onto Lattice Models

替代合金中的原子扩散和有序-无序相变是非常长的时间尺度现象，远远超出了分子动力学模拟的范围。这种现象可以在晶格气体模型中得到更有效的处理。基于一种全新的直觉，即原始非晶格系统的配分函数应该与晶格-气体模型的配分函数重合，我们提出了“势重正化理论”，它可以推导出相应的晶格-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CuxAu；1-x&Gt；合金。也就是说，我们借助于势重正化理论确定了不同温度下的相互作用参数，并用得到的相互作用参数对格子-气体模型进行了格子蒙特卡罗模拟。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较好。此外，得到的与不同成分x的CuxAU&lt；1-x&Gt；合金的有序-无序相变相关的相图很好地再现了实验相图。后者的结果最近发表在《晶体生长》杂志上。另一方面，我们将该理论应用到半柔性聚合物溶液的研究中，发现聚合物的刚性依赖于温度。我们在2003年10月8日至13日在横滨举行的ICAM-IUMRS上报告了这一情况。现在，将这种强大的方法应用于许多其他系统是非常可取的。

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.