Boettcher Stefan, Cook Jessica L, Ziff Robert M
Department of Physics, Emory University, Atlanta, Georgia 30322, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):041115. doi: 10.1103/PhysRevE.80.041115. Epub 2009 Oct 13.
The bond-percolation properties of the recently introduced Hanoi networks are analyzed with the renormalization group. Unlike scale-free networks, these networks are meant to provide an analytically tractable interpolation between finite-dimensional, lattice-based models and their mean-field limits. In percolation, the hierarchical small-world bonds in the Hanoi networks impose order by uniting otherwise disconnected, local clusters. This "patchy" order results in merely a finite probability to obtain a spanning cluster for certain ranges of the bond probability, unlike the usual 0-1 transition found on ordinary lattices. The various networks studied here exhibit a range of phase behaviors, depending on the prevalence of those long-range bonds. Fixed points in general exhibit nonuniversal behavior.
利用重整化群分析了最近引入的河内网络的键渗流特性。与无标度网络不同，这些网络旨在在有限维、基于晶格的模型及其平均场极限之间提供一个易于分析处理的插值。在渗流中，河内网络中的分层小世界键通过连接原本不相连的局部簇来引入秩序。这种“斑块状”秩序导致在键概率的某些范围内获得跨越簇的概率仅为有限值，这与普通晶格上常见的0 - 1转变不同。这里研究的各种网络表现出一系列的相行为，这取决于那些长程键的占比。一般来说，不动点表现出非普适行为。
