Tsakiris N, Maragakis M, Kosmidis K, Argyrakis P
Physics Department, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Oct;82(4 Pt 1):041108. doi: 10.1103/PhysRevE.82.041108. Epub 2010 Oct 11.
We study the percolation properties of the growing clusters model on a 2D square lattice. In this model, a number of seeds placed on random locations on the lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The model exhibits a discontinuous transition for very low values of the seed concentration p and a second, nontrivial continuous phase transition for intermediate p values. Here we study in detail this continuous transition that separates a phase of finite clusters from a phase characterized by the presence of a giant component. Using finite size scaling and large scale Monte Carlo simulations we determine the value of the percolation threshold where the giant component first appears, and the critical exponents that characterize the transition. We find that the transition belongs to a different universality class from the standard percolation transition.
我们研究二维正方形晶格上生长簇模型的渗流性质。在该模型中，放置在晶格随机位置上的一些种子以恒定速度生长以形成簇。当两个或更多簇最终相互接触时，它们会立即停止生长。对于非常低的种子浓度(p)，该模型呈现出不连续转变，而对于中间的(p)值，则呈现出第二个非平凡的连续相变。在此，我们详细研究这种将有限簇相和以存在巨型组分为特征的相分隔开的连续转变。通过有限尺寸标度和大规模蒙特卡罗模拟，我们确定巨型组分首次出现时的渗流阈值以及表征该转变的临界指数。我们发现该转变属于与标准渗流转变不同的普适类。
