1,616 research outputs found
Finite-size effects on the Hamiltonian dynamics of the XY-model
The dynamical properties of the finite-size magnetization M in the critical
region T<T_{KTB} of the planar rotor model on a L x L square lattice are
analyzed by means of microcanonical simulations . The behavior of the q=0
structure factor at high frequencies is consistent with field-theoretical
results, but new additional features occur at lower frequencies. The motion of
M determines a region of spectral lines and the presence of a central peak,
which we attribute to phase diffusion. Near T_{KTB} the diffusion constant
scales with system size as D ~ L^{-1.6(3)}.Comment: To be published in Europhysics Letter
Universal Fluctuations in Correlated Systems
The probability density function (PDF) of a global measure in a large class
of highly correlated systems has been suggested to be of the same functional
form. Here, we identify the analytical form of the PDF of one such measure, the
order parameter in the low temperature phase of the 2D-XY model. We demonstrate
that this function describes the fluctuations of global quantities in other
correlated, equilibrium and non-equilibrium systems. These include a coupled
rotor model, Ising and percolation models, models of forest fires, sand-piles,
avalanches and granular media in a self organized critical state. We discuss
the relationship with both Gaussian and extremal statistics.Comment: 4 pages, 2 figure
Electric Dipole Moments of Leptons in the Presence of Majorana Neutrinos
We calculate the two-loop diagrams that give a non-zero contribution to the
electric dipole moment d_l of a charged lepton l due to possible Majorana
masses of neutrinos. Using the example with one generation of the Standard
Model leptons and two heavy right-handed neutrinos, we demonstrate that the
non-vanishing result for d_l first appears in order O(m_l m_\nu^2 G_F^2), where
m_\nu is the mass of the light neutrino and the see-saw type relation is
imposed. This effect is beyond the reach of presently planned experiments.Comment: 13 page
Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model
We analyse the spin wave approximation for the 2D-XY model, directly in
reciprocal space. In this limit the model is diagonal and the normal modes are
statistically independent. Despite this simplicity non-trivial critical
properties are observed and exploited. We confirm that the observed asymmetry
for the probability density function for order parameter fluctuations comes
from the divergence of the mode amplitudes across the Brillouin zone. We show
that the asymmetry is a many body effect despite the importance played by the
zone centre. The precise form of the function is dependent on the details of
the Gibbs measure, giving weight to the idea that an effective Gibbs measure
should exist in non-equilibrium systems, if a similar distribution is observed.Comment: 12 pages, 9 figure
Towards Scalable Visual Exploration of Very Large RDF Graphs
In this paper, we outline our work on developing a disk-based infrastructure
for efficient visualization and graph exploration operations over very large
graphs. The proposed platform, called graphVizdb, is based on a novel technique
for indexing and storing the graph. Particularly, the graph layout is indexed
with a spatial data structure, i.e., an R-tree, and stored in a database. In
runtime, user operations are translated into efficient spatial operations
(i.e., window queries) in the backend.Comment: 12th Extended Semantic Web Conference (ESWC 2015
Finite size scaling in the 2D XY-model and generalized universality
In recent works (BHP), a generalized universality has been proposed, linking
phenomena as dissimilar as 2D magnetism and turbulence. To test these ideas, we
performed a MC study of the 2D XY-model. We found that the shape of the
probability distribution function for the magnetization M is non Gaussian and
independent of the system size --in the range of the lattice sizes studied--
below the Kosterlitz-Thoules temperature. However, the shape of these
distributions does depend on the temperature, contrarily to the BHP's claim.
This behavior is successfully explained by using an extended finite-size
scaling analysis and the existence of bounds for M.Comment: 7 pages, 5 figures. Submitted to Phys. Rev. Lett. Details of changes:
1. We emphasized in the abstract the range of validity of our results. 2. In
the last paragraph the temperature dependence of the PDF was slightly
re-formulate
Temperature dependent fluctuations in the two-dimensional XY model
We present a detailed investigation of the probability density function (PDF)
of order parameter fluctuations in the finite two-dimensional XY (2dXY) model.
In the low temperature critical phase of this model, the PDF approaches a
universal non-Gaussian limit distribution in the limit T-->0. Our analysis
resolves the question of temperature dependence of the PDF in this regime, for
which conflicting results have been reported. We show analytically that a weak
temperature dependence results from the inclusion of multiple loop graphs in a
previously-derived graphical expansion. This is confirmed by numerical
simulations on two controlled approximations to the 2dXY model: the Harmonic
and ``Harmonic XY'' models. The Harmonic model has no
Kosterlitz-Thouless-Berezinskii (KTB) transition and the PDF becomes
progressively less skewed with increasing temperature until it closely
approximates a Gaussian function above T ~ 4\pi. Near to that temperature we
find some evidence of a phase transition, although our observations appear to
exclude a thermodynamic singularity.Comment: 15 pages, 5 figures and 1 tabl
Hamiltonian Dynamics and the Phase Transition of the XY Model
A Hamiltonian dynamics is defined for the XY model by adding a kinetic energy
term. Thermodynamical properties (total energy, magnetization, vorticity)
derived from microcanonical simulations of this model are found to be in
agreement with canonical Monte-Carlo results in the explored temperature
region. The behavior of the magnetization and the energy as functions of the
temperature are thoroughly investigated, taking into account finite size
effects. By representing the spin field as a superposition of random phased
waves, we derive a nonlinear dispersion relation whose solutions allow the
computation of thermodynamical quantities, which agree quantitatively with
those obtained in numerical experiments, up to temperatures close to the
transition. At low temperatures the propagation of phonons is the dominant
phenomenon, while above the phase transition the system splits into ordered
domains separated by interfaces populated by topological defects. In the high
temperature phase, spins rotate, and an analogy with an Ising-like system can
be established, leading to a theoretical prediction of the critical temperature
.Comment: 10 figures, Revte
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