Study on Foundation and Applications of the Cluster Variation Method (CVM) and Path Probability Method (PPM)

项目“聚类变异法（CVM）和路径概率法（PPM）的基础及应用研究”的主要成果如下：(1)利用第一原理总能量计算得到的相互作用能与CVM结合，研究了贵金属合金的相图、有序不稳定性和近程有序参数的傅立叶谱。与四面体近似比较，得到了CVM四面体-八面体近似中k空间波动谱的正确特征。(2)在PPM的偶对近似下，采用固体对固体（SOS）模型研究了分子束外延条件下生长晶体的表面结构变化。发现原子空位对的平均数目周期性地变化，反映了一层一层的补全。(3)将CVM应用于具有随机相互作用的多组分系统。三组分体系在一定条件下发生玻璃化转变。(4)在PPM的四面体近似下研究了自旋体系的弛豫过程。在等温发展过程中，短暂地出现与最终平衡相不同的阶相。提出了“伪稳定状态”的概念。(5)研究了一维跳变模型的离子电导率。建立了电导率随频率变化的蒙特卡罗模拟方法，并与PPM方法进行了比较。(6)基于相干异常法（CAM），利用CVM和PPM的对、平方近似和平方近似，对D（= 2,3,4）维立方晶格Ising模型的二阶相变临界指数进行了解析研究。这些简单的近似给出了合理的临界指数值和正确的转变温度。

The main achievements concerning the project "Study on Foundation and Applications of the Cluster Variation Method (CVM) and Path Probability Method (PPM)" are itemized in the following ;(1) Interaction energies derived from the first-principle total energy calculation were used together with the CVM to study phase diagrams, ordering instability and the Fourier spectrum of the short range order parameters for noble metal alloys. The correct features of the k-space fluctuation spectrum is obtained in the tetrahedron-octahedron approximation of the CVM compared with the tetrahedron approximation.(2) The surface structure change of a growing crystal under the MBE (molecular beam epitaxy) condition is studied on the solid-on-solid (SOS) model in the pair approximation of the PPM. The average number of atom-vacancy pairs is found to change periodically, reflecting the layer-by-layer completion.(3) The CVM is applied to the multi-components system with random interaction. The glass transition is obtained under a certain condition in the three components system.(4) The relaxation process of spin system was investigated in the tetrahedron approximation of the PPM. In an isothermal development an order phase different from the final equilibrium one appears transiently. The concept of the "pseud-stable state" is proposed.(5) The ionic conductivity of 1D hopping model is studied. The Monte Carlo simulation method for the frequency dependent conductivity is developed and compared with the results obtained by the PPM.(6) The critical exponents of second order phase transition in the D (=2, 3, 4) dimensional cubic lattice Ising model was analytically studied on the basis of the coherent anomaly method (CAM) by using the pair, the square-cactus and the square approximation of the CVM and the PPM. These simple approximations give reasonable values of critical exponents and correct transition temperature.