193 research outputs found
Critical behavior of a fluid in a disordered porous matrix: An Ornstein-Zernike approach
Using a liquid-state approach based on Ornstein-Zernike equations, we study
the behavior of a fluid inside a porous disordered matrix near the liquid-gas
critical point.The results obtained within various standard approximation
schemes such as lowest-order -ordering and the mean-spherical
approximation suggest that the critical behavior is closely related to that of
the random-field Ising model (RFIM).Comment: 10 pages, revtex, to appear in Physical Review Letter
Critical Behavior of the 3d Random Field Ising Model: Two-Exponent Scaling or First Order Phase Transition?
In extensive Monte Carlo simulations the phase transition of the random field
Ising model in three dimensions is investigated. The values of the critical
exponents are determined via finite size scaling. For a Gaussian distribution
of the random fields it is found that the correlation length diverges
with an exponent at the critical temperature and that
with for the connected susceptibility
and with for
the disconnected susceptibility. Together with the amplitude ratio
being close to one this gives
further support for a two exponent scaling scenario implying
. The magnetization behaves discontinuously at the
transition, i.e. , indicating a first order transition. However, no
divergence for the specific heat and in particular no latent heat is found.
Also the probability distribution of the magnetization does not show a
multi-peak structure that is characteristic for the phase-coexistence at first
order phase transition points.Comment: 14 pages, RevTeX, 11 postscript figures (fig9.ps and fig11.ps should
be printed separately
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
extende
Full reduction of large finite random Ising systems by RSRG
We describe how to evaluate approximately various physical interesting
quantities in random Ising systems by direct renormalization of a finite
system. The renormalization procedure is used to reduce the number of degrees
of freedom to a number that is small enough, enabling direct summing over the
surviving spins. This procedure can be used to obtain averages of functions of
the surviving spins. We show how to evaluate averages that involve spins that
do not survive the renormalization procedure. We show, for the random field
Ising model, how to obtain the "connected" 2-spin correlation function and the
"disconnected" 2-spin correlation function. Consequently, we show how to obtain
the average susceptibility and the average energy. For an Ising system with
random bonds and random fields we show how to obtain the average specific heat.
We conclude by presenting our numerical results for the average susceptibility
and the "connected" 2-spin correlation function along one of the principal
axes. (We believe this to be the first time, where the full three dimensional
correlation is calculated and not just parameters like Nu or Eta.) The results
for the average susceptibility are used to extract the critical temperature and
critical exponents of the 3D random field Ising system.Comment: 30 pages, 17 figure
Lower Neutrino Mass Bound from SN1987A Data and Quantum Geometry
A lower bound on the light neutrino mass is derived in the framework
of a geometrical interpretation of quantum mechanics. Using this model and the
time of flight delay data for neutrinos coming from SN1987A, we find that the
neutrino masses are bounded from below by eV, in
agreement with the upper bound
eV currently available. When the model is applied to photons with effective
mass, we obtain a lower limit on the electron density in intergalactic space
that is compatible with recent baryon density measurements.Comment: 22 pages, 3 figure
Anderson-Mott transition as a quantum glass problem
We combine a recent mapping of the Anderson-Mott metal-insulator transition
on a random-field problem with scaling concepts for random-field magnets to
argue that disordered electrons near an Anderson-Mott transition show
glass-like behavior. We first discuss attempts to interpret experimental
results in terms of a conventional scaling picture, and argue that some of the
difficulties encountered point towards a glassy nature of the electrons. We
then develop a general scaling theory for a quantum glass, and discuss critical
properties of both thermodynamic and transport variables in terms of it. Our
most important conclusions are that for a correct interpretation of experiments
one must distinguish between self-averaging and non-self averaging observables,
and that dynamical or temperature scaling is not of power-law type but rather
activated, i.e. given by a generalized Vogel-Fulcher law. Recent mutually
contradicting experimental results on Si:P are discussed in the light of this,
and new experiments are proposed to test the predictions of our quantum glass
scaling theory.Comment: 25pp, REVTeX, 5 ps figs, final version as publishe
Tricritical Points in the Sherrington-Kirkpatrick Model in the Presence of Discrete Random Fields
The infinite-range-interaction Ising spin glass is considered in the presence
of an external random magnetic field following a trimodal (three-peak)
distribution. The model is studied through the replica method and phase
diagrams are obtained within the replica-symmetry approximation. It is shown
that the border of the ferromagnetic phase may present first-order phase
transitions, as well as tricritical points at finite temperatures. Analogous to
what happens for the Ising ferromagnet under a trimodal random field, it is
verified that the first-order phase transitions are directly related to the
dilution in the fields (represented by ). The ferromagnetic boundary at
zero temperature also exhibits an interesting behavior: for , a single tricritical point occurs, whereas if
the critical frontier is completely continuous; however, for
, a fourth-order critical point appears. The stability
analysis of the replica-symmetric solution is performed and the regions of
validity of such a solution are identified; in particular, the Almeida-Thouless
line in the plane field versus temperature is shown to depend on the weight
.Comment: 23pages, 7 ps figure
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