41 research outputs found
Comment on "Non-Mean-Field Behavior of the Contact Process on Scale-Free Networks"
Recently, Castellano and Pastor-Satorras [1] utilized the finite size scaling
(FSS) theory to analyze simulation data for the contact process (CP) on
scale-free networks (SFNs) and claimed that its absorbing critical behavior is
not consistent with the mean-field (MF) prediction. Furthermore, they pointed
out large density fluctuations at highly connected vertices as a possible
origin for non-MF critical behavior. In this Comment, we propose a scaling
theory for relative density fluctuations in the spirit of the MF theory, which
turns out to explain simulation data perfectly well. We also measure the value
of the critical density decay exponent, which agrees well with the MF
prediction. Our results strongly support that the CP on SFNs still exhibits a
MF-type critical behavior.Comment: 1 page, 2 figures, typos are correcte
Relevance of Abelian Symmetry and Stochasticity in Directed Sandpiles
We provide a comprehensive view on the role of Abelian symmetry and
stochasticity in the universality class of directed sandpile models, in context
of the underlying spatial correlations of metastable patterns and scars. It is
argued that the relevance of Abelian symmetry may depend on whether the dynamic
rule is stochastic or deterministic, by means of the interaction of metastable
patterns and avalanche flow. Based on the new scaling relations, we conjecture
critical exponents for avalanche, which is confirmed reasonably well in
large-scale numerical simulations.Comment: 4 pages, 3 figures; published versio