Critical Phenomena on Fractal Lattices
Critical Phenomena on Fractal Lattices
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DOI：
10.1103/physrevlett.45.855
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发表时间：
1980-09
影响因子：
8.6
通讯作者：
Y. Gefen;B. Mandelbrot;A. Aharony
中科院分区：
文献类型：
--
作者：
Y. Gefen;B. Mandelbrot;A. Aharony
将重整化群技术应用于若干自相似分形格位上的ising模型自旋。所得到的临界性质随（非整数）分形维数D而变化，但也与几个拓扑因素有关：分枝、连通性、空隙性等。对于任意$Dg~1$，存在既${T}_{c}=0$，又${T}_{c}g0$的系统；因此，没有定义较低的临界维数。${T}_{c}$的非消失值和临界指数取决于所有这些因素。
Renormalization-group techniques are applied to Ising-model spins placed on the sites of several self-similar fractal lattices. The resulting critical properties are shown to vary with the (noninteger) fractal dimensionality $D$, but also with several topological factors: ramification, connectivity, lacunarity, etc. For any $Dg~1$, there exist systems with both ${T}_{c}=0$, and ${T}_{c}g0$; hence a lower critical dimensionality is not defined. The nonvanishing values of ${T}_{c}$ and the critical exponents depend on all these factors.