3,093 research outputs found
Ising model on the Apollonian network with node dependent interactions
This work considers an Ising model on the Apollonian network, where the
exchange constant between two neighboring spins
is a function of the degree of both spins. Using the exact
geometrical construction rule for the network, the thermodynamical and magnetic
properties are evaluated by iterating a system of discrete maps that allows for
very precise results in the thermodynamic limit. The results can be compared to
the predictions of a general framework for spins models on scale-free networks,
where the node distribution , with node dependent
interacting constants. We observe that, by increasing , the critical
behavior of the model changes, from a phase transition at for a
uniform system , to a T=0 phase transition when : in the
thermodynamic limit, the system shows no exactly critical behavior at a finite
temperature. The magnetization and magnetic susceptibility are found to present
non-critical scaling properties.Comment: 6 figures, 12 figure file
Targeted Recovery as an Effective Strategy against Epidemic Spreading
We propose a targeted intervention protocol where recovery is restricted to
individuals that have the least number of infected neighbours. Our recovery
strategy is highly efficient on any kind of network, since epidemic outbreaks
are minimal when compared to the baseline scenario of spontaneous recovery. In
the case of spatially embedded networks, we find that an epidemic stays
strongly spatially confined with a characteristic length scale undergoing a
random walk. We demonstrate numerically and analytically that this dynamics
leads to an epidemic spot with a flat surface structure and a radius that grows
linearly with the spreading rate.Comment: 6 pages, 5 figure
Large cities are less green
We study how urban quality evolves as a result of carbon dioxide emissions as
urban agglomerations grow. We employ a bottom-up approach combining two
unprecedented microscopic data on population and carbon dioxide emissions in
the continental US. We first aggregate settlements that are close to each other
into cities using the City Clustering Algorithm (CCA) defining cities beyond
the administrative boundaries. Then, we use data on emissions at a
fine geographic scale to determine the total emissions of each city. We find a
superlinear scaling behavior, expressed by a power-law, between
emissions and city population with average allometric exponent
across all cities in the US. This result suggests that the high productivity of
large cities is done at the expense of a proportionally larger amount of
emissions compared to small cities. Furthermore, our results are substantially
different from those obtained by the standard administrative definition of
cities, i.e. Metropolitan Statistical Area (MSA). Specifically, MSAs display
isometric scaling emissions and we argue that this discrepancy is due to the
overestimation of MSA areas. The results suggest that allometric studies based
on administrative boundaries to define cities may suffer from endogeneity bias
Critical Behavior of a Three-State Potts Model on a Voronoi Lattice
We use the single-histogram technique to study the critical behavior of the
three-state Potts model on a (random) Voronoi-Delaunay lattice with size
ranging from 250 to 8000 sites. We consider the effect of an exponential decay
of the interactions with the distance,, with , and
observe that this system seems to have critical exponents and
which are different from the respective exponents of the three-state Potts
model on a regular square lattice. However, the ratio remains
essentially the same. We find numerical evidences (although not conclusive, due
to the small range of system size) that the specific heat on this random system
behaves as a power-law for and as a logarithmic divergence for
and Comment: 3 pages, 5 figure
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