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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】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】Real-space renormalization-group study of the phase transition in a Gaussian model of fractals
杨展如, Song Li, Z.R. Yang
PHYSICAL REVIEW E VOLUME 55, NUMBER 6 JUNE 1997,-0001,():
-1年11月30日
In this paper the phase transition of the Gaussian model on m-sheet fractals (mSG)l and (mDH)l is investigated by the real-space renormalization-group method, i.e., decimation following a spin rescaling. The latter is introduced to keep the parameter b constant. Fixed points of the renormalization-group transformation are found and discussed. Our results show the existence of different properties of phase transition between the Gaussian model and the Ising model on fractals. In addition, we find that the critical point k*=b/4 in a regular Sierpinski gasket is identified, with result of k*=b/d d is the coordination number! in Euclidean space. This indicates that the critical point of the Gaussian model may be uniquely determined by the coordination number whether on homogeneous fractals or translationally invariant 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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【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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