1,817 research outputs found
Phase Ordering Dynamics of Theory with Hamiltonian Equations of Motion
Phase ordering dynamics of the (2+1)- and (3+1)-dimensional theory
with Hamiltonian equations of motion is investigated numerically. Dynamic
scaling is confirmed. The dynamic exponent is different from that of the
Ising model with dynamics of model A, while the exponent is the same.Comment: to appear in Int. J. Mod. Phys.
Scaling laws for the largest Lyapunov exponent in long-range systems: A random matrix approach
We investigate the laws that rule the behavior of the largest Lyapunov
exponent (LLE) in many particle systems with long range interactions. We
consider as a representative system the so-called Hamiltonian alpha-XY model
where the adjustable parameter alpha controls the range of the interactions of
N ferromagnetic spins in a lattice of dimension d. In previous work the
dependence of the LLE with the system size N, for sufficiently high energies,
was established through numerical simulations. In the thermodynamic limit, the
LLE becomes constant for alpha greater than d whereas it decays as an inverse
power law of N for alpha smaller than d. A recent theoretical calculation based
on Pettini's geometrization of the dynamics is consistent with these numerical
results (M.-C. Firpo and S. Ruffo, cond-mat/0108158). Here we show that the
scaling behavior can also be explained by a random matrix approach, in which
the tangent mappings that define the Lyapunov exponents are modeled by random
simplectic matrices drawn from a suitable ensemble.Comment: 5 pages, no figure
Lyapunov exponent of many-particle systems: testing the stochastic approach
The stochastic approach to the determination of the largest Lyapunov exponent
of a many-particle system is tested in the so-called mean-field
XY-Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the
Lyapunov exponent to a few statistical properties of the Hessian matrix of the
interaction, which can be calculated as suitable thermal averages. We have
verified that there is a satisfactory quantitative agreement between theory and
simulations in the disordered phases of the XY models, either with attractive
or repulsive interactions. Part of the success of the theory is due to the
possibility of predicting the shape of the required correlation functions,
because this permits the calculation of correlation times as thermal averages.Comment: 11 pages including 6 figure
Lattice dynamics and phonon softening in Ni-Mn-Al Heusler alloys
Inelastic and elastic neutron scattering have been used to study a single
crystal of the NiMnAl Heusler alloy over a broad
temperature range. The paper reports the first experimental determination of
the low-lying phonon dispersion curves for this alloy system. We find that the
frequencies of the TA modes are relatively low. This branch exhibits an
anomaly (dip) at a wave number , which softens with
decreasing temperature. Associated with this anomalous dip at , an
elastic central peak scattering is also present. We have also observed
satellites due to the magnetic ordering.Comment: 6 pages, 6 figures. Accepted for publication in the Physical Review
Topological origin of the phase transition in a mean-field model
We argue that the phase transition in the mean-field XY model is related to a
particular change in the topology of its configuration space. The nature of
this topological transition can be discussed on the basis of elementary Morse
theory using the potential energy per particle V as a Morse function. The value
of V where such a topological transition occurs equals the thermodynamic value
of V at the phase transition and the number of (Morse) critical points grows
very fast with the number of particles N. Furthermore, as in statistical
mechanics, also in topology the way the thermodynamic limit is taken is
crucial.Comment: REVTeX, 5 pages, with 1 eps figure included. Some changes in the
text. To appear in Physical Review Letter
Premartensitic transition driven by magnetoelastic interaction in bcc ferromagnetic
We show that the magnetoelastic coupling between the magnetization and the
amplitude of a short wavelength phonon enables the existence of a first order
premartensitic transition from a bcc to a micromodulated phase in .
Such a magnetoelastic coupling has been experimentally evidenced by AC
susceptibility and ultrasonic measurements under applied magnetic field. A
latent heat around 9 J/mol has been measured using a highly sensitive
calorimeter. This value is in very good agreement with the value predicted by a
proposed model.Comment: 4 pages RevTex, 3 Postscript figures, to be published in Physical
Review Letter
To what extent can dynamical models describe statistical features of turbulent flows?
Statistical features of "bursty" behaviour in charged and neutral fluid
turbulence, are compared to statistics of intermittent events in a GOY shell
model, and avalanches in different models of Self Organized Criticality (SOC).
It is found that inter-burst times show a power law distribution for turbulent
samples and for the shell model, a property which is shared only in a
particular case of the running sandpile model. The breakdown of self-similarity
generated by isolated events observed in the turbulent samples, is well
reproduced by the shell model, while it is absent in all SOC models considered.
On this base, we conclude that SOC models are not adequate to mimic fluid
turbulence, while the GOY shell model constitutes a better candidate to
describe the gross features of turbulence.Comment: 14 pages, 4 figures, in press on Europhys. Lett. (may 2002
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