Juhász Róbert, Odor Géza
Research Institute for Solid State Physics and Optics, PO Box 49, H-1525 Budapest, Hungary.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):041123. doi: 10.1103/PhysRevE.80.041123. Epub 2009 Oct 21.
We present simulation results for the contact process on regular cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered that are characterized by different shortest-path dimensions and random-walk dimensions. We provide numerical evidence that an absorbing phase transition occurs at some finite value of the infection rate and the corresponding dynamical critical exponents depend on the underlying network. Furthermore, the time-dependent quantities exhibit log-periodic oscillations in agreement with the discrete scale invariance of the networks. In case of spreading from an initial active seed, the critical exponents are found to depend on the location of the initial seed and break the hyperscaling law of the directed percolation universality class due to the inhomogeneity of the networks. However, if the cluster-spreading quantities are averaged over initial sites, the hyperscaling law is restored.
我们给出了由一维晶格和一组长度无界的长边缘组成的规则立方网络上接触过程的模拟结果。考虑了具有不同长边缘集的网络，这些网络具有不同的最短路径维度和随机游走维度。我们提供了数值证据，表明在感染率的某个有限值处会发生吸收相变，并且相应的动力学临界指数取决于基础网络。此外，与网络的离散尺度不变性一致，随时间变化的量呈现对数周期振荡。在从初始活跃种子开始传播的情况下，发现临界指数取决于初始种子的位置，并且由于网络的不均匀性而打破了有向渗流普适类的超标度律。然而，如果在初始位点上对团簇传播量进行平均，则超标度律得以恢复。
