Cohen Reuven, Ben-Avraham Daniel, Havlin Shlomo
Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Sep;66(3 Pt 2A):036113. doi: 10.1103/PhysRevE.66.036113. Epub 2002 Sep 17.
We study the behavior of scale-free networks, having connectivity distribution P(k) approximately k(-lambda), close to the percolation threshold. We show that for networks with 3<lambda<4, known to undergo a transition at a finite threshold of dilution, the critical exponents are different than the expected mean-field values of regular percolation in infinite dimensions. Networks with 2<lambda<3 possess only a percolative phase. Nevertheless, we show that in this case percolation critical exponents are well defined, near the limit of extreme dilution (where all sites are removed), and that also then the exponents bear a strong lambda dependence. The regular mean-field values are recovered only for lambda>4.
我们研究了无标度网络的行为，其连通性分布(P(k))近似为(k^{-\lambda})，且接近渗流阈值。我们表明，对于(3 < \lambda < 4)的网络，已知其在有限稀释阈值处会发生转变，其临界指数不同于无限维中常规渗流的预期平均场值。(2 < \lambda < 3)的网络仅具有一个渗流相。然而，我们表明在这种情况下，渗流临界指数在接近极端稀释极限（即所有节点都被移除的情况）时是明确定义的，并且此时指数也呈现出强烈的(\lambda)依赖性。仅当(\lambda > 4)时才恢复常规平均场值。
