72 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
Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model
We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the
order parameter and its dynamic fluctuations near the onset of the
synchronization transition, paying particular attention to effects induced by
the randomness of the intrinsic frequencies of oscillators. For a population of
size , we study two ways of sampling the intrinsic frequencies according to
the {\it same} given unimodal distribution . In the `{\em random}'
case, frequencies are generated independently in accordance with ,
which gives rise to oscillator number fluctuation within any given frequency
interval. In the `{\em regular}' case, the frequencies are generated in a
deterministic manner that minimizes the oscillator number fluctuations, leading
to quasi-uniformly spaced frequencies in the population. We find that the two
samplings yield substantially different finite-size properties with clearly
distinct scaling exponents. Moreover, the hyperscaling relation between the
order parameter and its fluctuations is valid in the regular case, but is
violated in the random case. In this last case, a self-consistent mean-field
theory that completely ignores dynamic fluctuations correctly predicts the FSS
exponent of the order parameter but not its critical amplitude
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