https://doi.org/10.1140/epjb/e2012-20872-1
Regular Article
Continuous percolation phase transitions of two-dimensional lattice networks under a generalized Achlioptas process
1
Institute of Theoretical Physics, Chinese Academy of
Sciences, P.O. Box
2735, 100190
Beijing, P.R.
China
2
Key Laboratory of Cluster Science of Ministry of Education and
Department of Physics, Beijing Institute of Technology, 100081
Beijing, P.R.
China
a
e-mail: chenxs@itp.ac.cn
Received: 27 October 2011
Received in final form: 2 February 2012
Published online: 24 April 2012
The percolation phase transitions of two-dimensional lattice networks under a generalized Achlioptas process (GAP) are investigated. During the GAP, two edges are chosen randomly from the lattice and the edge with minimum product of the two connecting cluster sizes is taken as the next occupied bond with a probability p. At p = 0.5, the GAP becomes the random growth model and leads to the minority product rule at p = 1. Using the finite-size scaling analysis, we find that the percolation phase transitions of these systems with 0.5 ≤ p ≤ 1 are always continuous and their critical exponents depend on p. Therefore, the universality class of the critical phenomena in two-dimensional lattice networks under the GAP is related to the probability parameter p in addition.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2012
