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2005年06月21日

【期刊论文】Critical dynamics of the Gaussian model with multispin transitions

杨展如, Xiang-Mu Kong, , * and Z.R. Yang

PHYSICAL REVIEW E 67, 056121 (2003),-0001,():

-1年11月30日

摘要

In this paper, we present a multispin transition mechanism, which is an extension of the Glauber one, to investigate critical dynamics. By exactly solving the master equation, the influence of the multispin transition mechanism on the dynamic critical behavior is studied for the Gaussian model with nearest-neighbor interactions on d-dimensional lattices (d51, 2, and 3!. The time evolution of magnetization is exactly calculated, and the exact results of relaxation time and dynamic critical exponent are obtained. Our models are divided into two kinds: one is the spin-cluster transition and the other is the arbitrary multispin transition. It is found that there are different relaxation times, but the same dynamical critical exponent for different kinds of multispin transitions. The results show that the dynamical critical exponents are independent of spatial dimensions and configurations of transitional spins, and that the dynamical critical exponent is the same as that of the Glauber dynamics, and thus give a strong support to the simple single-spin-transition dynamics. Finally, we give a brief discussion on the results.

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2005年06月21日

【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

摘要

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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2005年06月21日

【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

摘要

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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2005年06月21日

【期刊论文】Phase transitions of the Ashkin-Teller model including antiferromagnetic interactions on a type of diamond hierarchical lattice

杨展如, Jian-Xin Le, , * and Z.R. Yang

PHYSICAL REVIEW E 69, 066107 (2004),-0001,():

-1年11月30日

摘要

Using the real-space renormalization-group transformation, we study the phase transitions of the Ashkin-Teller model including the antiferromagnetic interactions on a type of diamond hierarchical lattices, of which the number of bonds per branch of the generator is odd. The isotropic Ashkin-Teller model and the anisotropic one are, respectively, investigated. We find that the phase diagram, for the isotropic Ashkin-Teller model, consists of five phases, two of which are associated with the partially antiferromagnetic ordering of the system, while the phase diagram, for the anisotropic Ashkin-Teller model, contains 11 phases, six of which are related to the partially antiferromagnetic ordering of the system. The correlation length critical exponents and the crossover exponents are also calculated.

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2005年06月21日

【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

摘要

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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    北京师范大学,北京

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