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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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