67 research outputs found
Self-avoiding walks and connective constants in small-world networks
Long-distance characteristics of small-world networks have been studied by
means of self-avoiding walks (SAW's). We consider networks generated by
rewiring links in one- and two-dimensional regular lattices. The number of
SAW's was obtained from numerical simulations as a function of the number
of steps on the considered networks. The so-called connective constant,
, which characterizes the long-distance
behavior of the walks, increases continuously with disorder strength (or
rewiring probability, ). For small , one has a linear relation , and being constants dependent on the underlying
lattice. Close to one finds the behavior expected for random graphs. An
analytical approach is given to account for the results derived from numerical
simulations. Both methods yield results agreeing with each other for small ,
and differ for close to 1, because of the different connectivity
distributions resulting in both cases.Comment: 7 pages, 5 figure
Interface Motion and Pinning in Small World Networks
We show that the nonequilibrium dynamics of systems with many interacting
elements located on a small-world network can be much slower than on regular
networks. As an example, we study the phase ordering dynamics of the Ising
model on a Watts-Strogatz network, after a quench in the ferromagnetic phase at
zero temperature. In one and two dimensions, small-world features produce
dynamically frozen configurations, disordered at large length scales, analogous
of random field models. This picture differs from the common knowledge
(supported by equilibrium results) that ferromagnetic short-cuts connections
favor order and uniformity. We briefly discuss some implications of these
results regarding the dynamics of social changes.Comment: 4 pages, 5 figures with minor corrections. To appear in Phys. Rev.
Superconductor-insulator quantum phase transition in a single Josephson junction
The superconductor-to-insulator quantum phase transition in resistively
shunted Josephson junctions is investigated by means of path-integral Monte
Carlo simulations. This numerical technique allows us to directly access the
(previously unexplored) regime of the Josephson-to-charging energy ratios
E_J/E_C of order one. Our results unambiguously support an earlier theoretical
conjecture, based on renormalization-group calculations, that at T -> 0 the
dissipative phase transition occurs at a universal value of the shunt
resistance R_S = h/4e^2 for all values E_J/E_C. On the other hand,
finite-temperature effects are shown to turn this phase transition into a
crossover, which position depends significantly on E_J/E_C, as well as on the
dissipation strength and on temperature. The latter effect needs to be taken
into account in order to reconcile earlier theoretical predictions with recent
experimental results.Comment: 7 pages, 6 figure
Aharonov-Bohm oscillations of a particle coupled to dissipative environments
The amplitude of the Bohm-Aharonov oscillations of a particle moving around a
ring threaded by a magnetic flux and coupled to different dissipative
environments is studied. The decay of the oscillations when increasing the
radius of the ring is shown to depend on the spatial features of the coupling.
When the environment is modelled by the Caldeira-Leggett bath of oscillators,
or the particle is coupled by the Coulomb potential to a dirty electron gas,
interference effects are suppressed beyond a finite length, even at zero
temperature. A finite renormalization of the Aharonov-Bohm oscillations is
found for other models of the environment.Comment: 6 page
Two-loop approximation in the Coulomb blockade problem
We study Coulomb blockade (CB) oscillations in the thermodynamics of a
metallic grain which is connected to a lead by a tunneling contact with a large
conductance in a wide temperature range, ,
where is the charging energy. Using the instanton analysis and the
renormalization group we obtain the temperature dependence of the amplitude of
CB oscillations which differs from the previously obtained results. Assuming
that at the oscillation amplitude weakly depends on
temperature we estimate the magnitude of CB oscillations in the ground state
energy as .Comment: 10 pages, 3 figure
Nonequilibrium transitions in complex networks: a model of social interaction
We analyze the non-equilibrium order-disorder transition of Axelrod's model
of social interaction in several complex networks. In a small world network, we
find a transition between an ordered homogeneous state and a disordered state.
The transition point is shifted by the degree of spatial disorder of the
underlying network, the network disorder favoring ordered configurations. In
random scale-free networks the transition is only observed for finite size
systems, showing system size scaling, while in the thermodynamic limit only
ordered configurations are always obtained. Thus in the thermodynamic limit the
transition disappears. However, in structured scale-free networks, the phase
transition between an ordered and a disordered phase is restored.Comment: 7 pages revtex4, 10 figures, related material at
http://www.imedea.uib.es/PhysDept/Nonlinear/research_topics/Social
Transport Properties of Random Walks on Scale-Free/Regular-Lattice Hybrid Networks
We study numerically the mean access times for random walks on hybrid
disordered structures formed by embedding scale-free networks into regular
lattices, considering different transition rates for steps across lattice bonds
() and across network shortcuts (). For fast shortcuts () and
low shortcut densities, traversal time data collapse onto an universal curve,
while a crossover behavior that can be related to the percolation threshold of
the scale-free network component is identified at higher shortcut densities, in
analogy to similar observations reported recently in Newman-Watts small-world
networks. Furthermore, we observe that random walk traversal times are larger
for networks with a higher degree of inhomogeneity in their shortcut
distribution, and we discuss access time distributions as functions of the
initial and final node degrees. These findings are relevant, in particular,
when considering the optimization of existing information networks by the
addition of a small number of fast shortcut connections.Comment: 8 pages, 6 figures; expanded discussions, added figures and
references. To appear in J Stat Phy
Comparison of two non-primitive methods for path integral simulations: Higher-order corrections vs. an effective propagator approach
Two methods are compared that are used in path integral simulations. Both
methods aim to achieve faster convergence to the quantum limit than the
so-called primitive algorithm (PA). One method, originally proposed by
Takahashi and Imada, is based on a higher-order approximation (HOA) of the
quantum mechanical density operator. The other method is based upon an
effective propagator (EPr). This propagator is constructed such that it
produces correctly one and two-particle imaginary time correlation functions in
the limit of small densities even for finite Trotter numbers P. We discuss the
conceptual differences between both methods and compare the convergence rate of
both approaches. While the HOA method converges faster than the EPr approach,
EPr gives surprisingly good estimates of thermal quantities already for P = 1.
Despite a significant improvement with respect to PA, neither HOA nor EPr
overcomes the need to increase P linearly with inverse temperature. We also
derive the proper estimator for radial distribution functions for HOA based
path integral simulations.Comment: 17 pages, latex, 6 postscript figure
Introducing Small-World Network Effect to Critical Dynamics
We analytically investigate the kinetic Gaussian model and the
one-dimensional kinetic Ising model on two typical small-world networks (SWN),
the adding-type and the rewiring-type. The general approaches and some basic
equations are systematically formulated. The rigorous investigation of the
Glauber-type kinetic Gaussian model shows the mean-field-like global influence
on the dynamic evolution of the individual spins. Accordingly a simplified
method is presented and tested, and believed to be a good choice for the
mean-field transition widely (in fact, without exception so far) observed on
SWN. It yields the evolving equation of the Kawasaki-type Gaussian model. In
the one-dimensional Ising model, the p-dependence of the critical point is
analytically obtained and the inexistence of such a threshold p_c, for a finite
temperature transition, is confirmed. The static critical exponents, gamma and
beta are in accordance with the results of the recent Monte Carlo simulations,
and also with the mean-field critical behavior of the system. We also prove
that the SWN effect does not change the dynamic critical exponent, z=2, for
this model. The observed influence of the long-range randomness on the critical
point indicates two obviously different hidden mechanisms.Comment: 30 pages, 1 ps figures, REVTEX, accepted for publication in Phys.
Rev.
The Standard Model as a noncommutative geometry: the low energy regime
We render a thorough, physicist's account of the formulation of the Standard
Model (SM) of particle physics within the framework of noncommutative
differential geometry (NCG). We work in Minkowski spacetime rather than in
Euclidean space. We lay the stress on the physical ideas both underlying and
coming out of the noncommutative derivation of the SM, while we provide the
necessary mathematical tools. Postdiction of most of the main characteristics
of the SM is shown within the NCG framework. This framework, plus standard
renormalization technique at the one-loop level, suggest that the Higgs and top
masses should verify 1.3 m_top \lesssim m_H \lesssim 1.73 m_top.Comment: 44 pages, Plain TeX with AMS fonts, mass formulae readjusted, some
references added, to appear in Physics Report
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