用SU(2)的分立子群对SU(2)格点规范新作用量的Monte Carlo 模拟

我们用SU(2)的正二十面体分立子群对SU(2)格点规范理论的正弦作用量与指数作用量进行了Monte Carlo模拟。发现由分立子群本身产生的一阶相变点分别在β_c′≈9.2±0.2和β_c′=6.8±0.2。对方格能量和比热所得的结果与用SU(2)群所得的结果一致。从而证实了对以上两种作用量,用分立子群代替连续群的适用性,为以后进行计算时利用分立子群提供了依据。 关键词：     

SU(2)格点规范理论几种不同形式的作用量的Monte Carlo研究

对SU(2)格点规范理论用三种不同于常用形式的作用量进行了Monte Carlo模拟,计算了平均内能和比热。内能曲线都趋向共同的弱耦合极限,都有比热峰标志着临界点。观察到仅由于格点间隔α的高次幂项不同而引起临界点明显漂移的现象。 关键词：     

SU(2)格点规范理论一种新作用量的弦张力的Monte Carlo计算

在10⁴格点上我们对作用量为S_p=sin1-sin(1/2)TrU_p的SU(2)格点规范系统进行了Monte Carlo模拟,计算了弦张力σ和标度常数Δ₀²之比。计算还表明,元格的平均内能和比热峰对于格点体积的变化来说是稳定的。 关键词：     

MONTE CARLO STUDY OF THE TRIANGLE LATTICE GEUCHI-KAWAI MODEL

The triangle lattice Eguchi-Kawai model is studied by using the Monte Carlo technique. The results indicate that in the two-dimensional case U(1) symmetry is not broken but in the three-dimensional case a clear evidence of spontaneous breaking of the U(1) symmetry is observed in the weak coupling region.     

格点规范场论Monte Carlo模拟中一种节省时间的取样方法

我们在格点规范场理论的Monte Carlo模拟中引入了一种节省时间的取样方法,研究了该方法在Z₂规范群和SU(3)规范群临界点附近的行为,发现在越过一阶相变点时该方法将失效。按一定的程序,此特点可用来寻找一阶相变点。     

多自旋相互作用Ising模型相变类型的Monte Carlo研究

利用Monte Carlo方法,我们发现在水平方向上具有m自旋相互作用而在竖直方向具有n自旋相互作用的二维Ising模型。当m=n=3时,其相变是一级相变,而当m=3,n=2时,其相变却是二级相变。 关键词：     

MONTE CARLO STUDY OF MANTON'S ACTION FOR FOUR-DIMENSIONAL SU(5) LATTICE GAUGE THEORY

The feature of Manton's lattice action in the SU(5) four-dimensional lattice gauge theory is investigated by means of Monte Carlo simulation. A rather smooth curve of the internal energy is obtained, no discontinuity in the average action perplaquette is found in opposition to the resultes of usually adopted Wilson's action. An evidence of a higher order phase transition with Manton's action is also found.     

THE RADIOTHERAPEUTIC PLAN OF TUMOR INVESTIGATED BY MONTE CARLO METHOD

The optimization study of the radiotherapeutic plan by Monte Carlo method is discussed in this paper. The investigation results show that for a specific patient there must be an optimized radio-therapeutic plan, which includes the size, the direction and the energy of the incident γ-rays beam and the distance of the patient's skin from the irradiated source. It is pointed out in this paper that the isotope workers are challenged by the concept of radio-therapeutic science.     

铁磁键稀疏Blume-Capel模型相图的Monte Carlo研究

本文应用Monte Carlo方法求得铁磁键稀疏平方点阵的Blume-Capel模型的相图。利用有限尺寸的标度理论,得到晶场为零时的相变温度,并同其他方法所得的结果作了比较。同时用Monte Carlo方法确定了键稀疏时三临界点的值对键浓度的依赖关系。 关键词：     

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：     

三维随机点阵三态矢量Potts模型Monte Carlo模拟

在三维随机格点阵上对三态矢量Potts模型进行了Monte Carlo数值模拟,构造了N×N×N(N=8,10,12)三种不同大小点阵,分别计算了该自旋系统的能量密度、磁化强度、比热和磁化率等的温度曲线。结果表明该自旋系统在β₆≈0.16处存在着能表征一阶Z(3)对称破缺相变的能量热滞图和比热陡峰,磁化强度的跃变规律亦支持该结论,从而显示出该模型在随机点阵上的相变行为与正方点阵的已有结果的相似性。     

无损辨识时间依赖型内热源的 Monte Carlo方法

本文提出一种无损辨识时间依赖型内热源的Monte-Carlo算法,并成功地对两类不同形式的内热源进行了重构,结果证明了该算法的有效性.本文方法很容易推广到复杂的三维情形,也可推广用于空间依赖型内热源的无损辨识.     

SU(2)格点规范理论中的重夸克相互作用力及势的计算

本文用Monte Carlo方法对四维对称格点规范理论中具有较好标度性行为的单元格EXP作用量计算了重夸克-反夸克势。计算中利用了重整化群处理方法和SU(2)群的正二十面体子群近似。计算结果与维象的弦理论给出的库仑势加线性势的形式一致。 关键词：     

THE MC CALCULATION OF MASS GAP IN 2+1 DIMENSIONAL SU(2) LATTICE GAUGE THEORY

By combining Monte Carlo method and variational method,we calculate the mass gap of SU(2) lattice gauge theory in 18*18 lattice of 2+1 dimensions by means of the icosaheral subgroup (Y120) using a hamiltonian of which the ground state is exactly known.In the range 0<1/g²,we obtain the results which are in good agreement with analytical calculation of SU(2) group.The scaling behaviour of mass gap am=2.3g² is confirmed.     

THE PHASE TRANSITION FROM THE "ROTATION" TO VIBRATION SPECTRA IN THE LIPKIN SU(2) MODEL

The collective monopole excitation spectra of the Lipkin SU(2) model aresolveaexactly in the truncated monopole phonon representation and also approximately in the continuous variable representation. The transition from the "rotation" to vibration spectra for lowly-lying exclted states with the increase of the particle number in the upper level and the disappearance of the monopole "deformation" with the increase of the excitation energy are exhibited. The origin of these phase transitions is explained and the shape transition of real nuclei with the number of valence nucleons i s briefly discussed.     

巨正则量子Monte Carlo方法和二维Hubbard模型的研究

用巨正则量子Monte Carlo方法,计算了二维单带Hubbard模型的局域磁矩、磁化率、交错磁化率和内能等物理量.结果表明,用巨正则量子Monte Carlo方法能够统一地研究Hubbard模型的关联强度从弱至强区域的性质,它是处理强关联多体系统的有效方法.     

VARIATIONAL TREATMENT WITH THE THIRD ORDER CORRECTIONS FOR SU(2) LATTICE GAUGE THEORY

The variational method in Lagrangian formalism in lattice gauge theory in cumulant expansion is discussed. For SU(2) pure gauge Wi1son model to the third order corrections we show that there is no phase transition in four dimensions, but there exists the first order phase transition in five dimensions at β_C=0.838 in agreement with the Monte Carlo results. The physical meaning of higher order corrections is discussed.     

关于SU(2)规范场的结构

最近,吴大峻、杨振宁发现在Abel的U(1)规范场的情况下,磁荷的量子化数值与纤维丛的示性数相对应。但是在SU(2)规范场的情况下,由于球面上的SU(2)丛只有一种类型,于是必须寻找另外的拓扑不变关系,用它的特征类来区分具有不同单磁极的规范场。在文献[2]中我们曾注意到单磁极与SU(2)规范场的电荷算符的同位旋方向的拓扑关系,本文进一步结合SU(2)纤维丛及其U(1)子丛的关系,研究SU(2)规范场的分类。     

用细胞自动机方法构造非平衡相变模型

阐述了一旦给定细胞自动机方法的法则,将如何构造实际问题的物理学模型的方法。并用此法构造出非平衡相变模型。同时对类平均场近似方法进行了讨论,并将其预言与非平衡相变模型的精确的数值结果进行了比较。 关键词：     

A MONTE CARLO RENORMALIZATION GROUP STUDY OF A 2-DIMENSIONAL TRIANGULAR LATTICE

The method developed by D.J.E.Callaway is applied to Ising model on a two-dimensional triangular lattice. A fixed point and critical exponent are found. The results are consistent with one of the exact theories very well. Obviously this method show superiority to that obtained by some other approximate methods. The method is also applied to Z₂ gauge theory on a 2-dimensional triangular lattice, no fixed points are found, in agreement with other methods.