特殊钻石型等级晶格上S4模型的临界性质

应用实空间重整化群和累积展开的方法,研究了外场中特殊钻石型等级晶格上S4模型的相变和临界性质,求出了系统的临界点和临界指数. 结果表明,此系统除了存在一个Gauss不动点外,还存在一个Wilson-Fisher不动点,与该等级晶格上的Gauss模型相比较,系统的临界指数发生了变化.     

X分形晶格上Gauss模型的临界性质

采用实空间重整化群变换的方法,研究了2维和d(d>2)维X分形晶格上Gauss模型的临界性质.结果表明:这种晶格与其他分形晶格一样,在临界点处,其最近邻相互作用参量也可以表示为K=bqiqi(qi是格点i的配位数,bqi是格点i上自旋取值的Gauss分布常数)的形式;其关联长度临界指数v与空间维数d(或分形维数df)有关.这与Ising模型的结果存在很大的差异. 关键词： X分形晶格 重整化群 Gauss模型 临界性质     

Sierpinski镂垫上具有三体自旋作用的Gauss模型

应用实空间重整化群变换和累积展开相结合的方法，在Sierpinski镂垫上研究了二体自旋作用和三体自旋作用都存在时Gauss模型的相变和临界性质，求出了临界点和临界指数.与只有二体自旋作用的情况相比较，在无外场和有外场的情况下，临界点和临界指数都发生了变化，这表明三体自旋作用对其临界点和临界性质都有一定的影响. 关键词： Sierpinski镂垫 Gauss模型 重整化群 临界性质     

三维钻石型等级晶格上量子Heisenberg系统的临界性质

利用重整化群方法,研究了三维钻石型等级晶格上的各向异性量子Heisenberg模型,获得了系统的相图和临界性质. 结果表明:对于铁磁系统,在各向同性Heisenberg极限下,系统存在有限温度的相变,并计算了系统的序参量和临界指数; 对于反铁磁系统,在各向同性Heisenberg极限下,临界温度不等于零,在临界线上不存在重入行为.     

一簇金刚石晶格上S~4模型的相变

采用重整化群和累积展开的方法,研究了一簇金刚石晶格上S~4模型的相变,求得了系统的临界点.结果表明:当分支数m=2和m 12时,该系统只存在一个Gauss不动点K~*=b_2/2, u_2~*=0;当分支数3≤m≤12时,该系统不仅有Gauss不动点,还存在一个Wilson-Fisher不动点,并且后一个不动点对系统的临界特性产生决定性的影响.     

非均匀无序系统中Anderson局域化的标度理论——实空间重整化群途径

针对大量具有空间调制的无序系统,本文提出一种实空间重整化群变换方案。这个方案保证了在空间映象下相对的空间调制结构不变,因此可用以研究非均匀无序系统Anderson局域化的临界性质。在有限晶格近似下,我们对无序金属超晶格的一个简化模型求解了RG方程,得到不动点和临界指数的近似值,并发现空间调制在一定程度上引起无序系统电子局域化性质的改变。 关键词：     

Sierpinski 地毯上S4模型的临界特性

通过键移动重整化群的方法, 分析了Sierpinski 地毯上S⁴模型的临界行为, 得到了系统的临界点. 由得到的结果可知, 本系统不仅有一个高斯不动点, 而且还存在着一个Wilson Fisher不动点, 把它与Sierpinski 地毯上的高斯模型相互对比, 发现本系统的临界点变化很大. 这说明这两个系统隶属于两个不同的普适类.     

Sierpinski铺垫上Gaussian自旋系统的临界动力学研究

在单自旋跃迁临界动力学的基础上,利用动力学decimation重整化群技术,在考虑类磁型微扰的情况下,对动力学Gaussian自旋模型在具有扩展对称性的Sierpinski铺垫上的临界慢化行为进行了研究.结果表明,系统的动力学临界指数z仅与静态关联长度临界指数ν有关,而与分形维数Df无关.     

Sierpinski铺垫上Gaussian自旋系统的临界动力学研究

在单自旋跃迁临界动力学的基础上,利用动力学decimation重整化群技术,在考虑类磁型微扰的情况下,对动力学Gaussian自旋模型在具有扩展对称性的Sierpinski铺垫上的临界慢化行为进行了研究.结果表明,系统的动力学临界指数z仅与静态关联长度临界指数ν有关,而与分形维数D_f无关.     

T—H模型临界面的确定和相变研究

运用实空间重整化群得到了六角格子上T-H模型的相变流图、非平凡不动点、热指数等。用平均场自洽方程组确定了T-H模型的一级相变、二级相变临界面及三临界点。由r-△变换严格给出了T-H模型的临界面和部分临界指数。 关键词：     

Critical Behavior of the Gaussian Model with Periodic Interactions on Diamond—Type Hierarchical Lattices in External Magnetic Fields

The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences.The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction onds.The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method.The critical points and all the critical exponents are obtained.The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices.When all the Gaussian distribution constants are the same,the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.     

Triviality of Hierarchical Models with Small Negative φ4 Coupling in Four Dimensions

The Kadanoff-Wilson renormalization group (RG) for a class of hierarchical spin models including small negative φ⁴ terms in four dimensions are studied by using Gawędzki and Kupiainen's analysis. We prove triviality for the class, namely prove existence of critical trajectory that leads to the Gaussian fixed point.     

Triviality of Hierarchical Ising Model¶in Four Dimensions

Existence of critical renormalization group trajectory for a hierarchical Ising model in 4 dimensions is shown. After 70 iterations of renormalization group transformations, the critical Ising model is mapped into a vicinity of the Gaussian fixed point. Convergence of the subsequent trajectory to the Gaussian fixed point is shown by power decay of the effective coupling constant. The analysis in the strong coupling regime is computer-aided and Newman's inequalities on truncated correlations are used to give mathematical rigor to the numerical bounds. In order to obtain a criterion for convergence to the Gaussian fixed point, characteristic functions and Newman's inequalities are systematically used. Received: 27 April 2000 / Accepted: 5 January 2001     

On the large-N limit of 3D and 4D hermitian matrix models

The large-N limit of the hermitian matrix model in three and four euclidean space-time dimensions is studied with the help of the approximate Renormalization Group recursion formula. The planar graphs contributing to wave-function, mass and coupling-constant renormalization are identified and summed in this approximation. In four dimensions the model fails to have an interacting continuum limit, but in three dimensions there is a non-trivial fixed point for the approximate RG relations. The critical exponents of the three-dimensional model at this fixed point are ν = 0.67 and η = 0.20. The existence (or non-existence) of the fixed point and the critical exponents display a fairly high degree of universality since they do not seem to depend on the specific (non-universal) assumptions made in the approximation.     

Triviality of Hierarchical O(N) Spin Model in Four Dimensions with Large N

The renormalization group transformation for the hierarchical O(N) spin model in four dimensions is studied by means of characteristic functions of single-site measures, and convergence of the critical trajectory to the Gaussian fixed point is shown for a sufficiently large N. In the strong coupling regime, the trajectory is controlled by the help of the exactly solved O(∞) trajectory, while, in the weak coupling regime, convergence to the Gaussian fixed point is shown by power decay of the effective coupling constant.     

Bond dilution in the 3D Ising model: a Monte Carlo study

We study by Monte Carlo simulations the influence of bond dilution on the three-dimensional Ising model. This paradigmatic model in its pure version displays a second-order phase transition with a positive specific heat critical exponent . According to the Harris criterion disorder should hence lead to a new fixed point characterized by new critical exponents. We have determined the phase diagram of the diluted model, starting from the pure model limit down to the neighbourhood of the percolation threshold. For the estimation of critical exponents, we have first performed a finite-size scaling study, where we concentrated on three different dilutions to check the stability of the disorder fixed point. We emphasize in this work the great influence of the cross-over phenomena between the pure, disorder and percolation fixed points which lead to effective critical exponents dependent on the concentration. In a second set of simulations, the temperature behaviour of physical quantities has been studied in order to characterize the disorder fixed point more accurately. In particular this allowed us to estimate ratios of some critical amplitudes. In accord with previous observations for other models this provides stronger evidence for the existence of the disorder fixed point since the amplitude ratios are more sensitive to the universality class than the critical exponents. Moreover, the question of non-self-averaging at the disorder fixed point is investigated and compared with recent results for the bond-diluted q = 4 Potts model. Overall our numerical results provide evidence that, as expected on theoretical grounds, the critical behaviour of the bond-diluted model is indeed governed by the same universality class as the site-diluted model.Received: 24 February 2004, Published online: 28 May 2004PACS: 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 64.60.Fr Equilibrium properties near critical points, critical exponents - 75.10.Hk Classical spin models