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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】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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杨展如, Zhuo Gao and Z.R. Yang,
PHYSICAL REVIEW E VOLUME 60, NUMBER 3 SEPTEMBER 1999,-0001,():
-1年11月30日
A catalytic reaction model, the Ziff-Gulari-Barshad model, is studied on fractal lattices, and the influence of the order of ramification of the lattice on the dynamic behavior of the model is investigated. According to the Monte Carlo simulation results, the order of ramification of the lattice is not crucial to the existence of the continuous transition. This is different from the equilibrium phase transitions in discrete-symmetry spin models such as the Ising model!. Our results indicate that the criterion of the existence of the reactive phase may be complicated.
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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】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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