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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,():

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摘要/描述

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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版权说明:以下全部内容由杨展如上传于   2005年06月21日 18时38分19秒,版权归本人所有。

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