630 research outputs found
Comment on "Universal Fluctuations in Correlated Systems"
This is a Comment on "Universal Fluctuations in Correlated Systems".Comment: to appear in Phys. Rev. Let
Universal Fluctuations of the Danube Water Level: a Link with Turbulence, Criticality and Company Growth
A global quantity, regardless of its precise nature, will often fluctuate
according to a Gaussian limit distribution. However, in highly correlated
systems, other limit distributions are possible. We have previously calculated
one such distribution and have argued that this function should apply
specifically, and in many instances, to global quantities that define a steady
state. Here we demonstrate, for the first time, the relevance of this
prediction to natural phenomena. The river level fluctuations of the Danube are
observed to obey our prediction, which immediately establishes a generic
statistical connection between turbulence, criticality and company growth
statistics.Comment: 5 pages, 1 figur
Ordered Phase of the Dipolar Spin Ice under [110]-Magnetic Fields
We find that the true ground state of the dipolar spin ice system under
[110]-magnetic fields is the ``Q=X'' structure, which is consistent with both
experiments and Monte Carlo simulations. We then perform a Monte Carlo
simulation to confirm that there exists a first order phase transition under
the [110]-field. In particular this result indicates the existence of the first
order phase transition to the ``Q=X'' phase in the field above 0.35 T for
Dy2Ti2O7. We also show the magnetic field-temperature phase diagram to
summarize the ordered states of this system.Comment: 4 pages, 5 figures, in RevTex4, submitted to J. Phys. Soc. Jp
Statistics of extremal intensities for Gaussian interfaces
The extremal Fourier intensities are studied for stationary
Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We
calculate the probability distribution of the maximal intensity and find that,
generically, it does not coincide with the distribution of the integrated power
spectrum (i.e. roughness of the surface), nor does it obey any of the known
extreme statistics limit distributions. The Fisher-Tippett-Gumbel limit
distribution is, however, recovered in three cases: (i) in the non-dispersive
(white noise) limit, (ii) for high dimensions, and (iii) when only
short-wavelength modes are kept. In the last two cases the limit distribution
emerges in novel scenarios.Comment: 15 pages, including 7 ps figure
Universal Magnetic Fluctuations with a Field Induced Length Scale
We calculate the probability density function for the order parameter
fluctuations in the low temperature phase of the 2D-XY model of magnetism near
the line of critical points. A finite correlation length, \xi, is introduced
with a small magnetic field, h, and an accurate expression for \xi(h) is
developed by treating non-linear contributions to the field energy using a
Hartree approximation. We find analytically a series of universal non-Gaussian
distributions with a finite size scaling form and present a Gumbel-like
function that gives the PDF to an excellent approximation. We propose the
Gumbel exponent, a(h), as an indirect measure of the length scale of
correlations in a wide range of complex systems.Comment: 7 pages, 4 figures, 1 table. To appear in Phys. Rev.
1/f Noise and Extreme Value Statistics
We study the finite-size scaling of the roughness of signals in systems
displaying Gaussian 1/f power spectra. It is found that one of the extreme
value distributions (Gumbel distribution) emerges as the scaling function when
the boundary conditions are periodic. We provide a realistic example of
periodic 1/f noise, and demonstrate by simulations that the Gumbel distribution
is a good approximation for the case of nonperiodic boundary conditions as
well. Experiments on voltage fluctuations in GaAs films are analyzed and
excellent agreement is found with the theory.Comment: 4 pages, 4 postscript figures, RevTe
Low Temperature Spin Freezing in Dy2Ti2O7 Spin Ice
We report a study of the low temperature bulk magnetic properties of the spin
ice compound Dy2Ti2O7 with particular attention to the (T < 4 K) spin freezing
transition. While this transition is superficially similar to that in a spin
glass, there are important qualitative differences from spin glass behavior:
the freezing temperature increases slightly with applied magnetic field, and
the distribution of spin relaxation times remains extremely narrow down to the
lowest temperatures. Furthermore, the characteristic spin relaxation time
increases faster than exponentially down to the lowest temperatures studied.
These results indicate that spin-freezing in spin ice materials represents a
novel form of magnetic glassiness associated with the unusual nature of
geometrical frustration in these materials.Comment: 24 pages, 8 figure
Long Range Order at Low Temperature in Dipolar Spin Ice
Recently it has been suggested that long range magnetic dipolar interactions
are responsible for spin ice behavior in the Ising pyrochlore magnets and . We report here numerical
results on the low temperature properties of the dipolar spin ice model,
obtained via a new loop algorithm which greatly improves the dynamics at low
temperature. We recover the previously reported missing entropy in this model,
and find a first order transition to a long range ordered phase with zero total
magnetization at very low temperature. We discuss the relevance of these
results to and .Comment: New version of the manuscript. Now contains 3 POSTSCRIPT figures as
opposed to 2 figures. Manuscript contains a more detailed discussion of the
(i) nature of long-range ordered ground state, (ii) finite-size scaling
results of the 1st order transition into the ground state. Order of authors
has been changed. Resubmitted to Physical Review Letters Contact:
[email protected]
Magnetization distribution in the transverse Ising chain with energy flux
The zero-temperature transverse Ising chain carrying an energy flux j_E is
studied with the aim of determining the nonequilibrium distribution functions,
P(M_z) and P(M_x), of its transverse and longitudinal magnetizations,
respectively. An exact calculation reveals that P(M_z) is a Gaussian both at
j_E=0 and j_E not equal 0, and the width of the distribution decreases with
increasing energy flux. The distribution of the order-parameter fluctuations,
P(M_x), is evaluated numerically for spin-chains of up to 20 spins. For the
equilibrium case (j_E=0), we find the expected Gaussian fluctuations away from
the critical point while the critical order-parameter fluctuations are shown to
be non-gaussian with a scaling function Phi(x)=Phi(M_x/)=P(M_x)
strongly dependent on the boundary conditions. When j_E not equal 0, the system
displays long-range, oscillating correlations but P(M_x) is a Gaussian
nevertheless, and the width of the Gaussian decreases with increasing j_E. In
particular, we find that, at critical transverse field, the width has a
j_E^(-3/8) asymptotic in the j_E -> 0 limit.Comment: 8 pages, 5 ps figure
Models with short and long-range interactions: phase diagram and reentrant phase
We study the phase diagram of two different Hamiltonians with competiting
local, nearest-neighbour, and mean-field couplings. The first example
corresponds to the HMF Hamiltonian with an additional short-range interaction.
The second example is a reduced Hamiltonian for dipolar layered spin
structures, with a new feature with respect to the first example, the presence
of anisotropies. The two examples are solved in both the canonical and the
microcanonical ensemble using a combination of the min-max method with the
transfer operator method. The phase diagrams present typical features of
systems with long-range interactions: ensemble inequivalence, negative specific
heat and temperature jumps. Moreover, in a given range of parameters, we report
the signature of phase reentrance. This can also be interpreted as the presence
of azeotropy with the creation of two first order phase transitions with
ensemble inequivalence, as one parameter is varied continuously
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