共查询到19条相似文献,搜索用时 265 毫秒
1.
2.
3.
4.
5.
6.
分形格点是一类特殊的格点,它具有非整数的维度,且打破了平移不变性.本文对分形格点中伊辛模型的临界行为进行了研究.在这个系统中存在从有序到无序的连续相变,本文利用张量网络重正化群算法计算了不同位置格点上的物理量,并据此在不同空间位置拟合出了相应的临界指数.由于平移对称性的缺失,发现临界指数的拟合结果对空间位置有依赖关系.另外,在分形格点中的不同位置检验了临界指数间的标度关系(hyperscaling relations),最终发现在某些格点上所有的标度关系全部成立,而在另外一些格点上则只有部分的标度关系成立. 相似文献
7.
8.
9.
10.
11.
The decimation real-space renormalization group and spin-rescaling methods are applied to the study of phase transition of the Gaussian model on fractal lattices. It is found that the critical point K* equals b/2 ( b is the distribution constant of Gaussian model) on nonbranching Koch curves. For inhomogeneous fractal lattices, it is proposed that the b is replaced with bqi (qi is the coordination number of the site i) and satisfies a certain relation bqi/bqj = qi/qj. Under this supposition we find that the critical point of the Gaussian model on a branching Koch curve can be expressed uniquely as K* = bqi/qi. 相似文献
12.
Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and d-dimensional (d > 2) Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality d (or the fractal dimensionality dr). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices. 相似文献
13.
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. 相似文献
14.
The transition to turbulence via spatiotemporal intermittency is investigated for coupled maps defined on generalized Sierpinski gaskets, a class of deterministic fractal lattices. Critical exponents that characterize the onset of intermittency are computed as a function of the fractal dimension of the lattice. Windows of spatiotemporal intermittency are found as the coupling parameter is varied for lattices with a fractal dimension greater than two. This phenomenon is associated with a collective chaotic behavior of the fractal array of coupled maps. 相似文献
15.
Critical slowing down of the Gaussian spin system on diamond—type hierarchical lattices 总被引:1,自引:0,他引:1 下载免费PDF全文
Based on the single-spin transition critical dynamics, we have investigated the critical slowing down of the Gaussian spin model situated on the fractal family of diamond-type hierarchical lattices. We calculate the dynamical critical exponent z and the correlation-length critical exponent ν using the dynamical decimation renormalization-group technique. The result, together with some earlier ones, suggests us to conclude that on a wide range of geometries, zν=1 is the general relationship, while the two exponents depend on the specific structure. However, we have investigated for various lattices in an earlier paper, the system studied in this paper shows highly universal z=1/ν=2 independent of the structure and the dimensionality. 相似文献
16.
In this papel, we present two fractal aggregation models, line pattern seed model (model 1) and point pattern seed model (model 2), which are particle-cluster models. Using the current models, we investigate the critical transition in fractal aggregation processes in two dimensions, and suggest a method for finding the critical transition point. The computer simulation results show that the critical concentration is Pca=0.69±0.02 for model 1 and Pca=0.72±0.01 for model 2, critical fractal dimension. Dc= 1.71±0.06 for model 1 and Dc=1.66±0.07 for model 2, which are in good agreement with those of DLA model (D=5/3) and experimental data. The results also show that the critical transition point in two dimensions seems to be inilependent of the size of lattices and the initial seed patterns. The results seem to belong to the same universality class. 相似文献
17.
Alexander S. Balankin M.A. Martínez-Cruz M.D. Álvarez-Jasso M. Patiño-Ortiz J. Patiño-Ortiz 《Physics letters. A》2019,383(10):957-966
This Letter is focused on the impact of network topology on the site percolation. Specifically, we study how the site percolation threshold depends on the network dimensions (topological d and fractal D), degree of connectivity (quantified by the mean coordination number ), and arrangement of bonds (characterized by the connectivity index Q also called the ramification exponent). Using the Fisher's containment principle, we established exact inequalities between percolation thresholds on fractal networks contained in the square lattice. The values of site percolation thresholds on some fractal lattices were found by numerical simulations. Our findings suggest that the most relevant parameters to describe properly the values of site percolation thresholds on fractal networks contained in square lattice (Sierpiński carpets and Cantor tartans) and based on the square lattice (weighted planar stochastic fractal and Cantor lattices) are the mean coordination number and ramification exponent, but not the fractal dimension. Accordingly, we propose an empirical formula providing a good approximation for the site percolation thresholds on these networks. We also put forward an empirical formula for the site percolation thresholds on d-dimensional simple hypercubic lattices. 相似文献
18.
P. N. Timonin 《Journal of Experimental and Theoretical Physics》2004,99(5):1044-1053
Thermodynamics of the Potts model with an arbitrary number of states is analyzed for a class of hierarchical lattices of fractal dimension d > 1. In contrast to the case of crystal lattice, it is shown that all phase transitions on lattices of this type are of the second order. Critical exponents are determined, their dependence on structural parameters is examined, and scaling relations between them are established. A structural criterion for change in transition order is discussed for inhomogeneous systems. Application of the results to critical phenomena in phase transitions in dilute crystals and porous media is discussed. 相似文献
19.
We study the critical behaviour of the ferromagnetic Potts Model on families of fractal lattices called Sierpinski Carpets and Sierpinski Pastry Shells. We find the influence of geometrical parameters on critical temperature and thermal exponents, which confirms lacunarity as a relevant geometrical parameter in the definition of universality classes. We distinguish the inner surface structure from the bulk and study the influence of both structures independently. The phase diagram for the Pastry Shell family exhibit a crossover between bulk and surface behaviour which shows the increasing importance of the surface bonds on the full fractal geometry as the fractal dimension or the lacunarity is lowered. 相似文献