TY - JOUR
T1 - Explosive site percolation with a product rule
AU - Choi, Woosik
AU - Yook, Soon Hyung
AU - Kim, Yup
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/8/30
Y1 - 2011/8/30
N2 - We study the site percolation under Achlioptas process with a product rule in a two-dimensional square lattice. From the measurement of the cluster size distribution Ps, we find that Ps has a very robust power-law regime followed by a stable hump near the transition threshold. Based on the careful analysis on the Ps distribution, we show that the transition should be discontinuous. The existence of the hysteresis loop in order parameter also verifies that the transition is discontinuous in two dimensions. Moreover, we also show that the transition nature from the product rule is not the same as that from a sum rule in two dimensions.
AB - We study the site percolation under Achlioptas process with a product rule in a two-dimensional square lattice. From the measurement of the cluster size distribution Ps, we find that Ps has a very robust power-law regime followed by a stable hump near the transition threshold. Based on the careful analysis on the Ps distribution, we show that the transition should be discontinuous. The existence of the hysteresis loop in order parameter also verifies that the transition is discontinuous in two dimensions. Moreover, we also show that the transition nature from the product rule is not the same as that from a sum rule in two dimensions.
UR - http://www.scopus.com/inward/record.url?scp=80052511499&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.84.020102
DO - 10.1103/PhysRevE.84.020102
M3 - Article
C2 - 21928937
AN - SCOPUS:80052511499
SN - 1539-3755
VL - 84
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 2
M1 - 020102
ER -