镶嵌正方晶格上Ising模型的近似解

采用格点自旋消约方法,将具有最近邻和次近邻耦合作用的镶嵌正方Ising晶格变换成等效的具有最近邻、次近邻和四体耦合作用的正方Ising晶格,得到系统近似解的临界点在K′C=0.4406868.结果表明:在相变点最近邻耦合作用K1和次近邻耦合作用K2之间满足一定关系.如果只计及镶嵌正方Ising晶格的最近邻耦合作用K1,则其严格解的临界点在K1C=0.7635.由此可以推断在正方格点间安放两个自旋的双镶嵌正方Ising晶格,在只计及最近邻耦合作用情况下,也是严格可解的.     

自旋S=1座稀释蜂窝格子的伊辛模型

本文对于自旋S=1的淬灭座稀释蜂窝格子的伊辛模型,在约束条件exp(K)cosh(J)=1下,求得了系统的临界温度和磁化强度与自旋浓度之间的关系。 关键词：     

Union Jack晶格上伊辛模型的自由费密近似解

运用自由费密近似对Union Jack晶格上具有各向异性二体耦合作用及三体相互作用的伊辛模型进行了求解,得到了模型的自由能、自发磁矩和临界点方程。在耦合常数简化为正方晶格上的伊辛模型时,得到了与Onsager一致的解。     

A NUMBER OF THE PERMISSIBLE PHASES FOR ISING LATTICE

The catastrophe theory is applied to investigating the number of permissible phase for homogeneous-isotropic and homogeneous anisotropic Ising lattices.     

镶嵌正方晶格上具有次近邻耦合作用Ising模型的临界性质

采用部分格点自旋消约变换,将镶嵌正方晶格上具有最近邻耦合作用K1和次近邻耦合作用K2的Ising模型变换成等效的具有最近邻、次近邻和四体耦合作用的正方Ising晶格.发现系统的临界点在(K1C,K2C)=(0.5125,0.2134),由此决定系统的临界温度,幷讨论了系统的普适性.     

引入“鬼”场的二维次近邻正方格点渗流模型的重整化群方法研究

应用位置空间重整化群方法,对引入“鬼”场的二维次近邻正方格点渗流模型进行研究,得到临界值P_c和临界指数α,β,γ,ν,δ,η。     

三维随机点阵Ising模型的集团Monte Carlo方法模拟

为了解决Monte Carlo模拟中的临界慢化问题,应用S-W方法,对一维随机点阵的模型进行了研究。找到该系统的相变点为β_c=0.075±0.001,与此同时,在相变点附近研究了SW方法的动力学性质,计算得动力学临界指数z=0.74±0.03,结果表明,SW方法对克服三维随机点阵Ising模型的临界慢化是非常有效的。 关键词：     

三维晶格统计模型的一种封闭的近似解

引用四元数(或转动群的双值表示)推广处理二维晶格统计模型的无规行走法,为三维简立方晶格求得了统计配分函数的一个封闭的近似解析表达式。它在从零到无限大的温度区间内都成立,可以过渡到正确的二维结果,具有一个温度奇点、非对数型的比热奇异性和较好的高温展开系数。     

NUMERICAL STUDIES ON THE DYNAMICS OF DISORDERED VORTEX LATTICE

Flow behavior of the driven two-dimensional vortex lattice is numerically studied with different densities of randomly distributed pointlike pinning centers. Different features in the curves of velocity-force dependence are found between the elastic and plastic regimes. Scaling fit between force and velocity above the critical driving force can be obtained in the elastic regime but fails in the plastic regime. Transition from the lastic to plastic regimes is accompanied by maximum peaks in the differential curves of velocity-force dependence in the disordered vortex lattice.     

二维对流扩散方程的格子Boltzmann方法

给出了二维对流扩散方程的格子Boltzmann方法,用对流扩散方程中的对流系数和扩散系数确定了局哉平衡分布函数Chapman-Enskog展开中的可调参数,并对该方法进行了讨论. 关键词：     

CRITICAL TEMPERATURE FOR A MODEL QUASI-ONE-DIMENSIONAL DISORDERED SUPERCONDUCTOR

With the help of the decimation ansatz of the renormlization group, the dependence of critical temperature on a transverse magnetic field is calculated analytically for a quasi-one-dimensional disordered superconductor model, based on the de Gennes-Skal-Shklovskii (dGSS) picture of the large cluster in a percolation system. Our results are in good agreement with those given by Halley's scaling theory.     

面心立方格子上自旋S=1的Ising反铁磁体的基态研究

本文发展了文献[1]中提出的利用费密变换求Ising模型基态的方法,根据由费密变换后,激发态能量大于零求得相边界,提出了直接比较各真空态能量来求解各基态的相边界。采用此方法,研究了具有近邻对相互作用的最一般的自旋S=1的Ising反铁磁体模型,严格地求得它在面心立方格子上的基态能量和零温相图。同时,还利用多相点方程,将参数k,l平面分成60个小区域,它们分别对应于各个拓扑不等价的零温相图。 关键词：     

THEORETICAL STUDY OF THE GROUND-STATE PROPERTY OF THE TWO-DIMENSIONAL HEISENBERG ANTIFERROMAGNET ON A TRIANGULAR LATTICE

Within the Tyablikov's theoretical framework, the ground-state property of the two-dimensional antiferromagnetic Heisenberg model on a triangular lattice is studied. Our results show that the sublattice magnetization is M=0.241 and the ground-state energy per bond is E_g/ NZJ =-0.166, which are in agreement with the numerical simulations.     

格子Boltzmann亚格子模型的研究

为了将格子Boltzmann法应用于大雷诺数流动的模拟,本文将Smagorinsky亚格子模型和LBGK模型相结合,并对该亚格子LBM模型进行了研究。利用该亚格子LBM模型,对二维顶盖驱动流进行了模拟,得到了若干大雷诺数下流线图和方腔中心线上无量纲速度分布。计算结果与基准解进行比较,两者相互吻合。     

Ising晶格系统可容纳的相数

我们应用突变论:(Catastrophe theory)讨论了均匀各向同性和均匀非各向同性Ising晶格系统可容纳相数的问题。d=3的Ising晶格系统至少可容纳三个相。 关键词：     

一维Fibonacci准周期Frustrated Ising模型的热力学特性

分别给出周期和自由边界条件下求解一维Fibonacci准周期Frustrated Ising模型的配分函数的方法。研究它的低温热力学性质,发现当温度趋于零时,其热力学函数在参数b/J=2/(2m+1)(m为正整数)处发生尖锐的变化。分析了零温时系统在不同参数范围内的基态构形,对计算的结果进行了解释。 关键词：     

双导带Anderson晶格的Slave-Boson平均场理论

应用Slave-Boson技术和泛函积分方法,处理了双导带Anderson晶格模型。在鞍点近似下,求得了系统的电子态密度和一些低温热力学量。结果表明,由于系统的相干性和f-c混合作用,电子态密度在费密面附近出现赝能隙结构。系统的低温热力学量具有重费密子特性。 关键词：     

FERRIMAGNETIC PHASES OF THE BLUME-EMERY-GRIFFITHS MODEL AND THE POTTS MODEL ON THE DIAMOND LATTICE

The phase transitions in the Blume-Emery-Griffiths (BEG) model and antiferromagnetic Potts model on the diamond lattice are investigated using the cluster-variation method in the pair approximation. The ferrimagnetic phases are found to be different from those on the simple-cubic lattice. The phase diagrams of the BEG model are also calculated. In the vicinity of the parameter line where the BEG model reduces to the three-state antiferromagnetic Potts model, new types of phase diagram are obtained. The results are different from those of the mean-field theory, which is a good approximation only for large coordination number of the lattice.     

二维随机三角点阵上三态和四态Potts模型的蒙特—卡罗重整化群研究

本文用改进的蒙特-卡罗重整化群方法对二维随机三角点阵上的三态和四态Potts模型进行研究,分析它们的固定点及临界指数,所得的临界指数与理论的分析值符合很好。     

AN EXACT SOLUTION OF THE NAIVE SCHWINGER MODEL ON LATTICE

An exact solution of the Naive Schwinger model on lattice is found.The continuous limit of the solution is discussed.The result is that the Naive lattice gauge theory can not cut off the unphysical states of the Schwinger model in the high-energy limit.