TY - JOUR
T1 - Phase transition without global ordering in a hierarchical scale-free network
AU - Hasegawa, Takehisa
AU - Sato, Masataka
AU - Nemoto, Koji
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/1/9
Y1 - 2012/1/9
N2 - We study the site-bond percolation on a hierarchical scale-free network, namely, the decorated (2,2)-flower, by using the renormalization group technique. The phase diagram essentially depends on the fraction of occupied sites. Surprisingly, when each site is unoccupied even with a small probability, the system permits neither the percolating phase nor the nonpercolating phase, but rather only critical phases. Although the order parameter always remains zero, a transition still exists between the critical phases that is characterized by the value of the fractal exponent, which measures the degree of criticality; the system changes from one critical state to another with the jump of the fractal exponent at the transition point. The phase boundary depends on the fraction of occupied sites. When the fraction of unoccupied sites exceeds a certain value, the transition line between the critical phases disappears, and a unique critical phase remains.
AB - We study the site-bond percolation on a hierarchical scale-free network, namely, the decorated (2,2)-flower, by using the renormalization group technique. The phase diagram essentially depends on the fraction of occupied sites. Surprisingly, when each site is unoccupied even with a small probability, the system permits neither the percolating phase nor the nonpercolating phase, but rather only critical phases. Although the order parameter always remains zero, a transition still exists between the critical phases that is characterized by the value of the fractal exponent, which measures the degree of criticality; the system changes from one critical state to another with the jump of the fractal exponent at the transition point. The phase boundary depends on the fraction of occupied sites. When the fraction of unoccupied sites exceeds a certain value, the transition line between the critical phases disappears, and a unique critical phase remains.
UR - http://www.scopus.com/inward/record.url?scp=84856527744&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84856527744&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.85.017101
DO - 10.1103/PhysRevE.85.017101
M3 - Article
C2 - 22400706
AN - SCOPUS:84856527744
VL - 85
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 1
M1 - 017101
ER -