杨展如
1、分形上的相变研究。2、几何相变。3、自旋系统的临界动力学。4、Dimer系统的统计研究。5、粒子系的聚变问题。
个性化签名
- 姓名:杨展如
- 目前身份:
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学术头衔:
博士生导师
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学科领域:
数理科学
- 研究兴趣:1、分形上的相变研究。2、几何相变。3、自旋系统的临界动力学。4、Dimer系统的统计研究。5、粒子系的聚变问题。
杨展如,北京师范大学物理系教授,博士生导师。曾任物理系主任,北京师范大学理论物理研究所所长,北京师范大学副校长(分管理科科研和研究生院),北京师范大学学术委员会副主任。曾任中国教育部科技委员会数理学部委员,中国物理学会第七届和第八届常务理事。1984--1996年任“中国物理快报”编委,现任“理论物理通讯”及“物理学进展”编委。迄今已培养博士生和硕士生30余人。研究领域发表学术论文约80篇,主要涉及:1、分形上的相变研究:给出了一个对“不均匀性”(lacunarity,描写分形几何的一个基本量)数学描述的改进的表示式;对前人有关分形上相变的普适性判据的困难和内在矛盾,提出普适性判据迄今是一个有待解决的问题;发现在金刚石型迭代格子上反铁磁Potts模型存在低温代数衰减相,证明了前人争论许久的预言;在各种不同分形晶格上对sing,AT,BEG,Gaussian等模型的相变进行了较深入的研究;编写出版“分形物理学”(上海科技教育出版社,1996)。2、几何相变:20世纪80年代初期对有方向的晶格动物的形状和大小进行了研究,并用临界指数对其进行了描述。3、自旋系统的临界动力学,对二维动力Ising模型用解析方法,采用切断近似研究了它的临界动力学;在现有Glauber和Kawasaki机制之外,提出了“多自旋跃进”机制;通过解析计算,精确求解动力Caussian模型的动力学临界指数Z,发现Z的数值与空间维数无关;研究了饱含长程作用的Caussian模型的临界动力学。4、Dimer系统的统计研究,研究了在不同晶格结构上不同模型上的dimer系统的非平衡相变;研究了分形晶格的两个基本几何参量不均匀性(lacunarity)和分叉度(order of ramification)对dimer系统的非平衡相变行为的影响。5、粒子系的聚变问题,在平均场理论框架内用解析求解方法研究了饱含聚变、产生、湮灭、分解等过程的集团演化行为,并计算了有关的标度指数。
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【期刊论文】Critical dynamics of the kinetic Glauber-Ising model on hierarchical lattices
杨展如, Xiang-Mu Kong, , * and Z.R. Yang
PHYSICAL REVIEW E 69, 016101 (2004),-0001,():
-1年11月30日
The critical dynamics of the kinetic Glauber-Ising model is studied on a family of the diamond-type hierarchical lattices with various branches. By carrying out the time-dependent real-space renormalizationgroup transformation to the master equation of the systems considered, the dynamic exponent is calculated. We find that the dynamic exponent depends on fractal dimension df or the branch number m in a generator, and that it increases with the increase of df or m. We notice that for the case of m51 one-dimensional spin chain, df51) our result z52 is the same as the exact result obtained by Glauber, and for the case of m52 the simplest one in the diamond-type hierarchical lattices, df52) the exponent z52.626 is higher than those of the two-dimensional regular lattice and the triangular lattice.
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【期刊论文】Size and shape of directed lattice animals
杨展如, S Redner and Z R Yangt
J. Phys. A: Math. Gen. 15 (1982) L177-L187. Printed in Great Britain,-0001,():
-1年11月30日
We use the position-space renormalisation group and exact enumeration methods to study configurational properties of directed lattice animals. These are clusters made up of directed bonds in which the'tail'of a new bond must be added to the 'head' of already existing bonds. Furthermore, the directed bonds have a net orientational order with respect to some preferred anisotropy axis. In the limit that the number of bonds N+CQ, directed animals become extremely anisotropic and two independent correlation lengths, one parallel and one perpendicular to the preferred axis, are required to describe their shape. Mean-field theory suggests that these lengths diverge with exponents of Y I I=f and vl=$ respectively. Below seven dimensions mean-field theory breaks down, and we analyse our enumeration data to estimate the location of the critical point, the exponents YII and v l, and the exponent 0 characterising the singularity of the directed animal generating function. In two dimensions, we estimate that YH=0.8, vl=0.5 and 0=0.5, and our estimates interpolate smoothly with dimension to their respective mean-field limits. In two dimensions, we also apply a one-parameter position-space renormalisation group using small cells which gives reasonable estimates for the location of the critical point and q. In addition, we formulate a two-parameter renormalisation which allows us to study animals with a variable fraction of directed bonds, and thereby describe the crossover between directed and isotropic animals. We find that any anisotropy ensures that the critical behaviour belongs to the universality class of directed animals.
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【期刊论文】An approximate partition function of the Ising model on the Sierpinski gasket
杨展如, Z R Yang
J. Phys. A: Math. Gen. 20 (1987) 3019-3027. Printed in the U K,-0001,():
-1年11月30日
The partition function of the lsing model on the Sierpinski gasket is obtained by using a decoupled Sierpinski gasket Ising model as an unperturbed system. The exact partition function can be expressed as a statistical average of a special product over an unperturbed Ising Hamiltonian. A high-temperature expansion of the partition function is produced.
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【期刊论文】Lacunarity and universality
杨展如, Ling Hao and Z R Yang
J. Phys. A: Math. Gen. 20 (1987) 1627-1631. Printed in the UK,-0001,():
-1年11月30日
Lacunarity as a criterion of universality in phase transitions on Sierpinski carpets is studied. The approximate theoretical and numerical results suggest that systems of different lacunarity may belong to a common universality class. There seems to be a lack of solutions to the complete set of universality criteria on Sierpinski carpets.
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【期刊论文】Diamond-type hierarchical lattices for the Potts antiferromagnet
杨展如, Yung Qin, Z.R. Yang
PHYSICAL REVIEW B VOLUME 43, NUMBER 10 1 APRIL 1991,-0001,():
-1年11月30日
The Potts antiferromagnet situated on the fractal family of diamond-type hierarchical lattices is investigated The exact analysis of our findings reveals that the algebraically ordered behavior pre- dicted by Berker and Kadanoff can exist on such lattices with L=odd, where L is the structure pa- rameter of the hierarchical lattices; however, similar behavior to that of the antiferromagnetic Potts model on a decorated square lattice is exhibited for systems with L=even. We find that the different constructions that have the same ffactal dimensionality can have a different cutoff value q 0, in contrast with the translationally invariant system. We also give the ground-state entropy at q=qo in a closed form for the systems with L=even.
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【期刊论文】Glauber dynamics of the kinetic Ising model
杨展如, Z.R. Yang
PHYSICAL REVIEW B VOLUME 46, NUMBER 18 1 NOVEMBER 1992-II,-0001,():
-1年11月30日
In this work we study the Glauber dynamics of the one-dimensional Ising model with nearest. neighbor and next-nearest-neighbor interactions,for which an approximate solution of the magnetiza-tion per site is obtained. When the dynamical critical exponent z is investigated following the treatment of Cordery,Sarker,and Tobochnik [Phys. Rev, B 24, 5402 (1981)], our observation shows that its upper. bound value is the same as the known value, thus implying that z is independent of the range of the in-teraction. We also suggest a high-temperature expansion approximation which is then used to solve the two-dimensional Glauber dynamics governed by a master equation; this solution is compared with that of the decoupling method. the time-delayed correlation function 1S also calculated.
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【期刊论文】Family of diamond-type hierarchical lattices
杨展如, Z.R. Yang
PHYSICAL REVIEW B VOLUME 38, NUMBER 1 1 JULY 1988,-0001,():
-1年11月30日
A family of the diamond-type hierarchical lattices as a kind of fractals is proposed, on which the Ising model is exactly solved. The convergent condition of the free energy per bond in the thermo- dynamic limit is obviously given. We find that the unstable fixed point of the renormalization-group transformation moves toward K=0 (T=οο) from K=οο(T=O) as the number of branches P iS in. creased, and when P=οο(i.e., df=οο) the unstable fixed point K=O exactly, in contrast with that of the Bethe lattice, We also calculate the critical exponent of the correlation length; we find that in the df=2 and 3 cases the exponent is different from that of the regular lattice with d=2 and 3. re- s19ectively, whmh seems to imply that more general criteria for the ClaSSlnCatlOn of UnlVerSalltV should be oroposed. We have also discussed the upper crmcal fractal dlmensmn.
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【期刊论文】Kinetic phase transition of the three-state-vector Potts model
杨展如, Danmei Chen, Z.R. Yang
PHYSICAL REVIEW E VOLUME 49, NUMBER 17 I MAY 1994-I,-0001,():
-1年11月30日
We have studied the kinetic phase transition of a three-state-vector Potts system on a triangular lattice in contact with a heat bath and subject to an external energy source. The system evolves via the stochas-tic dynamics composed of Glauber and Kawasaki dynamics simulating interaction with the heat bath and energy source, respectively. The pair approximation IS used. It 1S found that there IS a paramagnetic-ferromagnetic transition at small energy flow, and the transition line is obtained. Also, when the energy is large enough, the system always will be in the paramagnetic state.
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【期刊论文】Solvable Ising model 0n Sierpfnski carpets: The partition function
杨展如, Z.R. Yang
PHYSICAL REVIEW E VOLUME 49, NUMBER 3 MARCH 1994,-0001,():
-1年11月30日
With a special Sierpfnski carpet (SC),the Ising model is exactly solved by a combinatorial approach and graph technique. The rigorous partition function and free energy are obtained and the phase transi-tion is investigated. We argue that the existence of a phase transition strongly depends on the order of ramification of the SC. Our method is extended to deal with other lattices.
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【期刊论文】Multifractality of probability measure on energy-spectrum supports
杨展如, Z.R. Yang
PHYSICAL REVIEW E VOLUME 47, NUMBER 2 FEBRUARY 1993,-0001,():
-1年11月30日
We have studied quadric type energy (frequency) recursion relations resulting from fractal lattices. We found that the allowed energy intervals in successive levels form two similar two-scale Cantor sets. If WE imagine the iterating procedure as a dynamical process, the iterating results in different levels gen-erate a"time"sequence, and we can introduce an equal probability measure Pu on a Cantor set and con-struct,following Helsey et a1. [Phys. Rev. A 33, 1141 (1986)], a partition function F (q,T) =∑ipq/17; finally, we obtain Dq-q and f (a)-a curves. A number of exactly soluable examples are investigated.
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