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Investigation of quasi-periodic variations in hard X-rays of solar flares. II. Further investigation of oscillating magnetic traps
In our recent paper (Solar Physics 261, 233) we investigated quasi-periodic
oscillations of hard X-rays during impulsive phase of solar flares. We have
come to conclusion that they are caused by magnetosonic oscillations of
magnetic traps within the volume of hard-X-ray (HXR) loop-top sources. In the
present paper we investigate four flares which show clear quasi-periodic
sequences of HXR pulses. We also describe our phenomenological model of
oscillating magnetic traps to show that it can explain observed properties of
HXR oscillations. Main results are the following: 1. We have found that
low-amplitude quasi-periodic oscillations occur before impulsive phase of some
flares. 2. We have found that quasi-period of the oscillations can change in
some flares. We interpret this as being due to changes of the length of
oscillating magnetic traps. 3. During impulsive phase a significant part of the
energy of accelerated (non-thermal) electrons is deposited within the HXR
loop-top source. 4. Our analysis suggests that quick development of impulsive
phase is due to feedback between pulses of the pressure of accelerated
electrons and the amplitude of magnetic-trap oscillation. 5. We have also
determined electron number density and magnetic filed strength for HXR loop-top
sources of several flares. The values fall within the limits of cm, gauss.Comment: 18 pages, 14 figures, submitted to Solar Physic
Monte Carlo study of the random-field Ising model
Using a cluster-flipping Monte Carlo algorithm combined with a generalization
of the histogram reweighting scheme of Ferrenberg and Swendsen, we have studied
the equilibrium properties of the thermal random-field Ising model on a cubic
lattice in three dimensions. We have equilibrated systems of LxLxL spins, with
values of L up to 32, and for these systems the cluster-flipping method appears
to a large extent to overcome the slow equilibration seen in single-spin-flip
methods. From the results of our simulations we have extracted values for the
critical exponents and the critical temperature and randomness of the model by
finite size scaling. For the exponents we find nu = 1.02 +/- 0.06, beta = 0.06
+/- 0.07, gamma = 1.9 +/- 0.2, and gammabar = 2.9 +/- 0.2.Comment: 12 pages, 6 figures, self-expanding uuencoded compressed PostScript
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Emergence of Quantum Ergodicity in Rough Billiards
By analytical mapping of the eigenvalue problem in rough billiards on to a
band random matrix model a new regime of Wigner ergodicity is found. There the
eigenstates are extended over the whole energy surface but have a strongly
peaked structure. The results of numerical simulations and implications for
level statistics are also discussed.Comment: revtex, 4 pages, 4 figure
Percolation in three-dimensional random field Ising magnets
The structure of the three-dimensional random field Ising magnet is studied
by ground state calculations. We investigate the percolation of the minority
spin orientation in the paramagnetic phase above the bulk phase transition,
located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the
Gaussian random fields (J=1). With an external field H there is a disorder
strength dependent critical field +/- H_c(Delta) for the down (or up) spin
spanning. The percolation transition is in the standard percolation
universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/-
0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <=
Delta_p. When, with zero external field, Delta is decreased from a large value
there is a transition from the simultaneous up and down spin spanning, with
probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This
is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster
has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta).
We provide evidence that this is asymptotically true even at H=0 for Delta_c <
Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is
approached from above. Percolation implies extra finite size effects in the
ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review
Correlation functions in the two-dimensional random-field Ising model
Transfer-matrix methods are used to study the probability distributions of
spin-spin correlation functions in the two-dimensional random-field Ising
model, on long strips of width sites, for binary field
distributions at generic distance , temperature and field intensity
. For moderately high , and of the order of magnitude used in
most experiments, the distributions are singly-peaked, though rather
asymmetric. For low temperatures the single-peaked shape deteriorates, crossing
over towards a double- ground-state structure. A connection is obtained
between the probability distribution for correlation functions and the
underlying distribution of accumulated field fluctuations. Analytical
expressions are in good agreement with numerical results for ,
low , not too small, and near G=1. From a finite-size {\it ansatz} at
, , averaged correlation functions are predicted to
scale with , . From numerical data we estimate y=0.875 \pm
0.025WR/L=1W \sim h_0^{\kappa} f(L h_0^u)\kappa \simeq 0.45u \simeq 0.8f(x)x \to \inftyW \sim
h_0^{\kappa}d=2$.Comment: RevTeX code for 8 pages, 7 eps figures, to appear in Physical Review
E (1999
Local correlations of different eigenfunctions in a disordered wire
We calculate the correlator of the local density of states
in quasi-one-dimensional disordered wires
in a magnetic field, assuming that |r_1-r_2| is much smaller than the
localization length. This amounts to finding the zero mode of the
transfer-matrix Hamiltonian for the supersymmetric sigma-model, which is done
exactly by the mapping to the three-dimensional Coulomb problem. Both the
regimes of level repulsion and level attraction are obtained, depending on
|r_1-r_2|. We demonstrate that the correlations of different eigenfunctions in
the quasi-one-dimensional and strictly one-dimensional cases are dissimilar.Comment: 5 pages, 2 figures. v2: an error in treating the spatial dependence
of correlations is correcte
Noncollinear magnetic ordering in small Chromium Clusters
We investigate noncollinear effects in antiferromagnetically coupled clusters
using the general, rotationally invariant form of local spin-density theory.
The coupling to the electronic degrees of freedom is treated with relativistic
non-local pseudopotentials and the ionic structure is optimized by Monte-Carlo
techniques. We find that small chromium clusters (N \le 13) strongly favor
noncollinear configurations of their local magnetic moments due to frustration.
This effect is associated with a significantly lower total magnetization of the
noncollinear ground states, ameliorating the disagreement between Stern-Gerlach
measurements and previous collinear calculations for Cr_{12} and Cr_{13}. Our
results further suggest that the trend to noncollinear configurations might be
a feature common to most antiferromagnetic clusters.Comment: 9 pages, RevTeX plus .eps/.ps figure
Equilibrium random-field Ising critical scattering in the antiferromagnet Fe(0.93)Zn(0.07)F2
It has long been believed that equilibrium random-field Ising model (RFIM)
critical scattering studies are not feasible in dilute antiferromagnets close
to and below Tc(H) because of severe non-equilibrium effects. The high magnetic
concentration Ising antiferromagnet Fe(0.93)Zn(0.07)F2, however, does provide
equilibrium behavior. We have employed scaling techniques to extract the
universal equilibrium scattering line shape, critical exponents nu = 0.87 +-
0.07 and eta = 0.20 +- 0.05, and amplitude ratios of this RFIM system.Comment: 4 pages, 1 figure, minor revision
Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations
Exact ground states of three-dimensional random field Ising magnets (RFIM)
with Gaussian distribution of the disorder are calculated using
graph-theoretical algorithms. Systems for different strengths h of the random
fields and sizes up to N=96^3 are considered. By numerically differentiating
the bond-energy with respect to h a specific-heat like quantity is obtained,
which does not appear to diverge at the critical point but rather exhibits a
cusp. We also consider the effect of a small uniform magnetic field, which
allows us to calculate the T=0 susceptibility. From a finite-size scaling
analysis, we obtain the critical exponents \nu=1.32(7), \alpha=-0.63(7),
\eta=0.50(3) and find that the critical strength of the random field is
h_c=2.28(1). We discuss the significance of the result that \alpha appears to
be strongly negative.Comment: 9 pages, 9 figures, 1 table, revtex revised version, slightly
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