Bastas N, Kosmidis K, Giazitzidis P, Maragakis M
Department of Physics, University of Thessaloniki, 54124 Thessaloniki, Greece.
Department of Physics, University of Thessaloniki, 54124 Thessaloniki, Greece and School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Dec;90(6):062101. doi: 10.1103/PhysRevE.90.062101. Epub 2014 Dec 1.
In phase-transition phenomena, the estimation of the critical point is crucial for the calculation of the various critical exponents and the determination of the universality class they belong to. However, this is not an easy task, since a large amount of realizations is needed to eliminate the noise in the data. In this paper, we introduce a novel method for the simultaneous estimation of the critical point p(c) and the critical exponent β/ν, applied for the case of "explosive" bond percolation on two-dimensional square lattices and Erdös-Rényi networks. The results show that with only a few hundred realizations, it is possible to acquire accurate values for these quantities. Guidelines are given at the end for the applicability of the method to other cases as well.
在相变现象中，临界点的估计对于各种临界指数的计算以及它们所属普适类的确定至关重要。然而，这并非易事，因为需要大量的实现来消除数据中的噪声。在本文中，我们介绍了一种同时估计临界点(p(c))和临界指数(\beta/\nu)的新方法，该方法适用于二维正方形晶格和厄多斯 - 雷尼网络上的“爆炸式”键渗流情况。结果表明，仅通过几百次实现，就有可能获得这些量的准确值。最后还给出了该方法适用于其他情况的指导方针。
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