161 research outputs found
Network harness: bundles of routes in public transport networks
Public transport routes sharing the same grid of streets and tracks are often
found to proceed in parallel along shorter or longer sequences of stations.
Similar phenomena are observed in other networks built with space consuming
links such as cables, vessels, pipes, neurons, etc. In the case of public
transport networks (PTNs) this behavior may be easily worked out on the basis
of sequences of stations serviced by each route. To quantify this behavior we
use the recently introduced notion of network harness. It is described by the
harness distribution P(r,s): the number of sequences of s consecutive stations
that are serviced by r parallel routes. For certain PTNs that we have analyzed
we observe that the harness distribution may be described by power laws. These
power laws observed indicate a certain level of organization and planning which
may be driven by the need to minimize the costs of infrastructure and secondly
by the fact that points of interest tend to be clustered in certain locations
of a city. This effect may be seen as a result of the strong interdependence of
the evolutions of both the city and its PTN.
To further investigate the significance of the empirical results we have
studied one- and two-dimensional models of randomly placed routes modeled by
different types of walks. While in one dimension an analytic treatment was
successful, the two dimensional case was studied by simulations showing that
the empirical results for real PTNs deviate significantly from those expected
for randomly placed routes.Comment: 12 pages, 24 figures, paper presented at the Conference ``Statistical
Physics: Modern Trends and Applications'' (23-25 June 2009, Lviv, Ukaine)
dedicated to the 100th anniversary of Mykola Bogolyubov (1909-1992
The McCoy-Wu Model in the Mean-field Approximation
We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu
model) and study its critical properties in the frame of mean-field theory. In
the low-temperature phase there is an average spontaneous magnetization in the
system, which vanishes as a power law at the critical point with the critical
exponents and in the bulk and at the
surface of the system, respectively. The singularity of the specific heat is
characterized by an exponent . The samples reduced
critical temperature has a power law distribution and we show that the difference between the values of the
critical exponents in the pure and in the random system is just . Above the critical temperature the thermodynamic quantities behave
analytically, thus the system does not exhibit Griffiths singularities.Comment: LaTeX file with iop macros, 13 pages, 7 eps figures, to appear in J.
Phys.
Historical and interpretative aspects of quantum mechanics: a physicists' naive approach
Many theoretical predictions derived from quantum mechanics have been
confirmed experimentally during the last 80 years. However, interpretative
aspects have long been subject to debate. Among them, the question of the
existence of hidden variables is still open. We review these questions, paying
special attention to historical aspects, and argue that one may definitively
exclude local realism on the basis of present experimental outcomes. Other
interpretations of Quantum Mechanics are nevertheless not excluded.Comment: 30 page
Finite temperature behavior of strongly disordered quantum magnets coupled to a dissipative bath
We study the effect of dissipation on the infinite randomness fixed point and
the Griffiths-McCoy singularities of random transverse Ising systems in chains,
ladders and in two-dimensions. A strong disorder renormalization group scheme
is presented that allows the computation of the finite temperature behavior of
the magnetic susceptibility and the spin specific heat. In the case of Ohmic
dissipation the susceptibility displays a crossover from Griffiths-McCoy
behavior (with a continuously varying dynamical exponent) to classical Curie
behavior at some temperature . The specific heat displays Griffiths-McCoy
singularities over the whole temperature range. For super-Ohmic dissipation we
find an infinite randomness fixed point within the same universality class as
the transverse Ising system without dissipation. In this case the phase diagram
and the parameter dependence of the dynamical exponent in the Griffiths-McCoy
phase can be determined analytically.Comment: 23 pages, 12 figure
Quasi-long-range ordering in a finite-size 2D Heisenberg model
We analyse the low-temperature behaviour of the Heisenberg model on a
two-dimensional lattice of finite size. Presence of a residual magnetisation in
a finite-size system enables us to use the spin wave approximation, which is
known to give reliable results for the XY model at low temperatures T. For the
system considered, we find that the spin-spin correlation function decays as
1/r^eta(T) for large separations r bringing about presence of a
quasi-long-range ordering. We give analytic estimates for the exponent eta(T)
in different regimes and support our findings by Monte Carlo simulations of the
model on lattices of different sizes at different temperatures.Comment: 9 pages, 3 postscript figs, style files include
The Fate of Ernst Ising and the Fate of his Model
On this, the occasion of the 20th anniversary of the "Ising Lectures" in Lviv
(Ukraine), we give some personal reflections about the famous model that was
suggested by Wilhelm Lenz for ferromagnetism in 1920 and solved in one
dimension by his PhD student, Ernst Ising, in 1924. That work of Lenz and Ising
marked the start of a scientific direction that, over nearly 100 years,
delivered extraordinary successes in explaining collective behaviour in a vast
variety of systems, both within and beyond the natural sciences. The broadness
of the appeal of the Ising model is reflected in the variety of talks presented
at the Ising lectures ( http://www.icmp.lviv.ua/ising/ ) over the past two
decades but requires that we restrict this report to a small selection of
topics. The paper starts with some personal memoirs of Thomas Ising (Ernst's
son). We then discuss the history of the model, exact solutions, experimental
realisations, and its extension to other fields.Comment: 46 pages, 9 figure
Transportation Network Stability: a Case Study of City Traffic
The goals of this paper are to present criteria, that allow to a priori
quantify the attack stability of real world correlated networks of finite size
and to check how these criteria correspond to analytic results available for
infinite uncorrelated networks. As a case study, we consider public
transportation networks (PTN) of several major cities of the world. To analyze
their resilience against attacks either the network nodes or edges are removed
in specific sequences (attack scenarios). During each scenario the size S(c) of
the largest remaining network component is observed as function of the removed
share c of nodes or edges. To quantify the PTN stability with respect to
different attack scenarios we use the area below the curve described by S(c)
for c \in [0,1] recently introduced (Schneider, C. M, et al., PNAS 108 (2011)
3838) as a numerical measure of network robustness. This measure captures the
network reaction over the whole attack sequence. We present results of the
analysis of PTN stability against node and link-targeted attacks.Comment: 18 pages, 7 figures. Submitted to the topical issue of the journal
'Advances in Complex Systems
Surface Properties of Aperiodic Ising Quantum Chains
We consider Ising quantum chains with quenched aperiodic disorder of the
coupling constants given through general substitution rules. The critical
scaling behaviour of several bulk and surface quantities is obtained by exact
real space renormalization.Comment: 4 pages, RevTex, reference update
Marginal Extended Perturbations in Two Dimensions and Gap-Exponent Relations
The most general form of a marginal extended perturbation in a
two-dimensional system is deduced from scaling considerations. It includes as
particular cases extended perturbations decaying either from a surface, a line
or a point for which exact results have been previously obtained. The
first-order corrections to the local exponents, which are functions of the
amplitude of the defect, are deduced from a perturbation expansion of the
two-point correlation functions. Assuming covariance under conformal
transformation, the perturbed system is mapped onto a cylinder. Working in the
Hamiltonian limit, the first-order corrections to the lowest gaps are
calculated for the Ising model. The results confirm the validity of the
gap-exponent relations for the perturbed system.Comment: 11 pages, Plain TeX, eps
Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model
We consider m two-dimensional semi-infinite planes of Ising spins joined
together through surface spins and study the critical behaviour near to the
junction. The m=0 limit of the model - according to the replica trick -
corresponds to the semi-infinite Ising model in the presence of a random
surface field (RSFI). Using conformal mapping, second-order perturbation
expansion around the weakly- and strongly-coupled planes limits and
differential renormalization group, we show that the surface critical behaviour
of the RSFI model is described by Ising critical exponents with logarithmic
corrections to scaling, while at multiple junctions (m>2) the transition is
first order. There is a spontaneous junction magnetization at the bulk critical
point.Comment: Old paper, for archiving. 6 pages, 1 figure, IOP macro, eps
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