866 research outputs found
Direct sampling of complex landscapes at low temperatures: the three-dimensional +/-J Ising spin glass
A method is presented, which allows to sample directly low-temperature
configurations of glassy systems, like spin glasses. The basic idea is to
generate ground states and low lying excited configurations using a heuristic
algorithm. Then, with the help of microcanonical Monte Carlo simulations, more
configurations are found, clusters of configurations are determined and
entropies evaluated. Finally equilibrium configuration are randomly sampled
with proper Gibbs-Boltzmann weights.
The method is applied to three-dimensional Ising spin glasses with +- J
interactions and temperatures T<=0.5. The low-temperature behavior of this
model is characterized by evaluating different overlap quantities, exhibiting a
complex low-energy landscape for T>0, while the T=0 behavior appears to be less
complex.Comment: 9 pages, 7 figures, revtex (one sentence changed compared to v2
An optimal network for passenger traffic
The optimal solution of an inter-city passenger transport network has been
studied using Zipf's law for the city populations and the Gravity law
describing the fluxes of inter-city passenger traffic. Assuming a fixed value
for the cost of transport per person per kilometer we observe that while the
total traffic cost decreases, the total wiring cost increases with the density
of links. As a result the total cost to maintain the traffic distribution is
optimal at a certain link density which vanishes on increasing the network
size. At a finite link density the network is scale-free. Using this model the
air-route network of India has been generated and an one-to-one comparison of
the nodal degree values with the real network has been made.Comment: 5 pages, 4 figure
The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
The nature of the zero temperature ordering transition in the 3D Gaussian
random field Ising magnet is studied numerically, aided by scaling analyses. In
the ferromagnetic phase the scaling of the roughness of the domain walls,
, is consistent with the theoretical prediction .
As the randomness is increased through the transition, the probability
distribution of the interfacial tension of domain walls scales as for a single
second order transition. At the critical point, the fractal dimensions of
domain walls and the fractal dimension of the outer surface of spin clusters
are investigated: there are at least two distinct physically important fractal
dimensions. These dimensions are argued to be related to combinations of the
energy scaling exponent, , which determines the violation of
hyperscaling, the correlation length exponent , and the magnetization
exponent . The value is derived from the
magnetization: this estimate is supported by the study of the spin cluster size
distribution at criticality. The variation of configurations in the interior of
a sample with boundary conditions is consistent with the hypothesis that there
is a single transition separating the disordered phase with one ground state
from the ordered phase with two ground states. The array of results are shown
to be consistent with a scaling picture and a geometric description of the
influence of boundary conditions on the spins. The details of the algorithm
used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure
Low Energy Excitations in Spin Glasses from Exact Ground States
We investigate the nature of the low-energy, large-scale excitations in the
three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and
free boundary conditions, by studying the response of the ground state to a
coupling-dependent perturbation introduced previously. The ground states are
determined exactly for system sizes up to 12^3 spins using a branch and cut
algorithm. The data are consistent with a picture where the surface of the
excitations is not space-filling, such as the droplet or the ``TNT'' picture,
with only minimal corrections to scaling. When allowing for very large
corrections to scaling, the data are also consistent with a picture with
space-filling surfaces, such as replica symmetry breaking. The energy of the
excitations scales with their size with a small exponent \theta', which is
compatible with zero if we allow moderate corrections to scaling. We compare
the results with data for periodic boundary conditions obtained with a genetic
algorithm, and discuss the effects of different boundary conditions on
corrections to scaling. Finally, we analyze the performance of our branch and
cut algorithm, finding that it is correlated with the existence of
large-scale,low-energy excitations.Comment: 18 Revtex pages, 16 eps figures. Text significantly expanded with
more discussion of the numerical data. Fig.11 adde
Binary data corruption due to a Brownian agent
We introduce a model of binary data corruption induced by a Brownian agent
(active random walker) on a d-dimensional lattice. A continuum formulation
allows the exact calculation of several quantities related to the density of
corrupted bits \rho; for example the mean of \rho, and the density-density
correlation function. Excellent agreement is found with the results from
numerical simulations. We also calculate the probability distribution of \rho
in d=1, which is found to be log-normal, indicating that the system is governed
by extreme fluctuations.Comment: 39 pages, 10 figures, RevTe
Space as a low-temperature regime of graphs
I define a statistical model of graphs in which 2-dimensional spaces arise at
low temperature. The configurations are given by graphs with a fixed number of
edges and the Hamiltonian is a simple, local function of the graphs.
Simulations show that there is a transition between a low-temperature regime in
which the graphs form triangulations of 2-dimensional surfaces and a
high-temperature regime, where the surfaces disappear. I use data for the
specific heat and other observables to discuss whether this is a phase
transition. The surface states are analyzed with regard to topology and
defects.Comment: 22 pages, 12 figures; v3: published version; J.Stat.Phys. 201
The Eigenvalue Analysis of the Density Matrix of 4D Spin Glasses Supports Replica Symmetry Breaking
We present a general and powerful numerical method useful to study the
density matrix of spin models. We apply the method to finite dimensional spin
glasses, and we analyze in detail the four dimensional Edwards-Anderson model
with Gaussian quenched random couplings. Our results clearly support the
existence of replica symmetry breaking in the thermodynamical limit.Comment: 8 pages, 13 postscript figure
Synchronization, Diversity, and Topology of Networks of Integrate and Fire Oscillators
We study synchronization dynamics of a population of pulse-coupled
oscillators. In particular, we focus our attention in the interplay between
networks topological disorder and its synchronization features. Firstly, we
analyze synchronization time in random networks, and find a scaling law
which relates to networks connectivity. Then, we carry on comparing
synchronization time for several other topological configurations,
characterized by a different degree of randomness. The analysis shows that
regular lattices perform better than any other disordered network. The fact can
be understood by considering the variability in the number of links between two
adjacent neighbors. This phenomenon is equivalent to have a non-random topology
with a distribution of interactions and it can be removed by an adequate local
normalization of the couplings.Comment: 6 pages, 8 figures, LaTeX 209, uses RevTe
Distributed flow optimization and cascading effects in weighted complex networks
We investigate the effect of a specific edge weighting scheme on distributed flow efficiency and robustness to cascading
failures in scale-free networks. In particular, we analyze a simple, yet
fundamental distributed flow model: current flow in random resistor networks.
By the tuning of control parameter and by considering two general cases
of relative node processing capabilities as well as the effect of bandwidth, we
show the dependence of transport efficiency upon the correlations between the
topology and weights. By studying the severity of cascades for different
control parameter , we find that network resilience to cascading
overloads and network throughput is optimal for the same value of over
the range of node capacities and available bandwidth
Extended droplet theory for aging in short-ranged spin glasses and a numerical examination
We analyze isothermal aging of a four dimensional Edwards-Anderson model in
detail by Monte Carlo simulations. We analyze the data in the view of an
extended version of the droplet theory proposed recently (cond-mat/0202110)
which is based on the original droplet theory plus conjectures on the
anomalously soft droplets in the presence of domain walls. We found that the
scaling laws including some fundamental predictions of the original droplet
theory explain well our results. The results of our simulation strongly suggest
the separation of the breaking of the time translational invariance and the
fluctuation dissipation theorem in agreement with our scenario.Comment: 27 pages, 39 epsfiles, revised versio
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