294 research outputs found
The two-dimensional random-bond Ising model, free fermions and the network model
We develop a recently-proposed mapping of the two-dimensional Ising model
with random exchange (RBIM), via the transfer matrix, to a network model for a
disordered system of non-interacting fermions. The RBIM transforms in this way
to a localisation problem belonging to one of a set of non-standard symmetry
classes, known as class D; the transition between paramagnet and ferromagnet is
equivalent to a delocalisation transition between an insulator and a quantum
Hall conductor. We establish the mapping as an exact and efficient tool for
numerical analysis: using it, the computational effort required to study a
system of width is proportional to , and not exponential in as
with conventional algorithms. We show how the approach may be used to calculate
for the RBIM: the free energy; typical correlation lengths in quasi-one
dimension for both the spin and the disorder operators; even powers of
spin-spin correlation functions and their disorder-averages. We examine in
detail the square-lattice, nearest-neighbour RBIM, in which bonds are
independently antiferromagnetic with probability , and ferromagnetic with
probability . Studying temperatures , we obtain precise
coordinates in the plane for points on the phase boundary between
ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We
demonstrate scaling flow towards the pure Ising fixed point at small , and
determine critical exponents at the multicritical point.Comment: 20 pages, 25 figures, figures correcte
Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
When the two-dimensional random-bond Ising model is represented as a
noninteracting fermion problem, it has the same symmetries as an ensemble of
random matrices known as class D. A nonlinear sigma model analysis of the
latter in two dimensions has previously led to the prediction of a metallic
phase, in which the fermion eigenstates at zero energy are extended. In this
paper we argue that such behavior cannot occur in the random-bond Ising model,
by showing that the Ising spin correlations in the metallic phase violate the
bound on such correlations that results from the reality of the Ising
couplings. Some types of disorder in spinless or spin-polarized p-wave
superconductors and paired fractional quantum Hall states allow a mapping onto
an Ising model with real but correlated bonds, and hence a metallic phase is
not possible there either. It is further argued that vortex disorder, which is
generic in the fractional quantum Hall applications, destroys the ordered or
weak-pairing phase, in which nonabelian statistics is obtained in the pure
case.Comment: 13 pages; largely independent of cond-mat/0007254; V. 2: as publishe
Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses
A huge number of independent true ground-state configurations is calculated
for two-, three- and four-dimensional +- J spin-glass models. Using the genetic
cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are
treated. A ``ballistic-search'' algorithm is applied which allows even for
large system sizes to identify clusters of ground states which are connected by
chains of zero-energy flips of spins. The number of clusters n_C diverges with
N going to infinity. For all dimensions considered here, an exponential
increase of n_C appears to be more likely than a growth with a power of N. The
number of different ground states is found to grow clearly exponentially with
N. A zero-temperature entropy per spin of s_0=0.078(5)k_B (2d), s_0=0.051(3)k_B
(3d) respectively s_0=0.027(5)k_B (4d) is obtained.Comment: large extensions, now 12 pages, 9 figures, 27 reference
Asymptotic Capture-Number and Island-Size Distributions for One-Dimensional Irreversible Submonolayer Growth
Using a set of evolution equations [J.G. Amar {\it et al}, Phys. Rev. Lett.
{\bf 86}, 3092 (2001)] for the average gap-size between islands, we calculate
analytically the asymptotic scaled capture-number distribution (CND) for
one-dimensional irreversible submonolayer growth of point islands. The
predicted asymptotic CND is in reasonably good agreement with kinetic
Monte-Carlo (KMC) results and leads to a \textit{non-divergent asymptotic}
scaled island-size distribution (ISD). We then show that a slight modification
of our analytical form leads to an analytic expression for the asymptotic CND
and a resulting asymptotic ISD which are in excellent agreement with KMC
simulations. We also show that in the asymptotic limit the self-averaging
property of the capture zones holds exactly while the asymptotic scaled gap
distribution is equal to the scaled CND.Comment: 4 pages, 1 figure, submitted to Phys. Rev.
Carrier induced ferromagnetism in diluted magnetic semi-conductors
We present a theory for carrier induced ferromagnetism in diluted magnetic
semi-conductor (DMS). Our approach treats on equal footing quantum fluctuations
within the RPA approximation and disorder within CPA. This method allows for
the calculation of , magnetization and magnon spectrum as a function of
hole, impurity concentration and temperature. It is shown that, sufficiently
close to , and within our decoupling scheme (Tyablicov type) the CPA for
the itinerant electron gas reduces to the Virtual Crystal Approximation. This
allows, in the low impurity concentration and low density of carriers to
provide analytical expression for . For illustration, we consider the case
of and compare our results with available experimental data.Comment: 5 figures included. to appear in Phys. Rev. B (brief report
Ohm's Law for Plasma in General Relativity and Cowling's Theorem
The general-relativistic Ohm's law for a two-component plasma which includes
the gravitomagnetic force terms even in the case of quasi-neutrality has been
derived. The equations that describe the electromagnetic processes in a plasma
surrounding a neutron star are obtained by using the general relativistic form
of Maxwell equations in a geometry of slow rotating gravitational object. In
addition to the general-relativistic effect first discussed by Khanna \&
Camenzind (1996) we predict a mechanism of the generation of azimuthal current
under the general relativistic effect of dragging of inertial frames on radial
current in a plasma around neutron star. The azimuthal current being
proportional to the angular velocity of the dragging of inertial
frames can give valuable contribution on the evolution of the stellar magnetic
field if exceeds (
is the number density of the charged particles, is the conductivity of
plasma). Thus in general relativity a rotating neutron star, embedded in
plasma, can in principle generate axial-symmetric magnetic fields even in
axisymmetry. However, classical Cowling's antidynamo theorem, according to
which a stationary axial-symmetric magnetic field can not be sustained against
ohmic diffusion, has to be hold in the general-relativistic case for the
typical plasma being responsible for the rotating neutron star.Comment: Accepted for publication in Astrophysics & Space Scienc
The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction across a tunneling junction out of equilibrium
The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic
- spin impurities across a tunneling junction is studied when the system
is driven out of equilibrium through biasing the junction. The nonequilibrium
situation is handled with the Keldysh time-loop perturbation formalism in
conjunction with appropriate coupling methods for tunneling systems due to
Caroli and Feuchtwang. We find that the presence of a nonequilibrium bias
across the junction leads to an interference of several fundamental
oscillations, such that in this tunneling geometry, it is possible to tune the
interaction between ferromagnetic and antiferromagnetic coupling at a fixed
impurity configuration, simply by changing the bias across the junction.
Furthermore, it is shown that the range of the RKKY interaction is altered out
of equilibrium, such that in particular the interaction energy between two
slabs of spins scales extensively with the thickness of the slabs in the
presence of an applied bias.Comment: 38 pages revtex preprint; 5 postscript figures; submitted to Phys.
Rev.
Particle acceleration in three-dimensional tearing configurations
In three-dimensional electromagnetic configurations that result from unstable
resistive tearing modes particles can efficiently be accelerated to
relativistic energies. To prove this resistive magnetohydrodynamic simulations
are used as input configurations for successive test particle simulations. The
simulations show the capability of three-dimensional non-linearly evolved
tearing modes to accelerate particles perpendicular to the plane of the
reconnecting magnetic field components. The simulations differ considerably
from analytical approaches by involving a realistic three-dimensional electric
field with a non-homogenous component parallel to the current direction. The
resulting particle spectra exhibit strong pitch-angle anisotropies. Typically,
about 5-8 % of an initially Maxwellian distribution is accelerated to the
maximum energy levels given by the macroscopic generalized electric potential
structure. Results are shown for both, non-relativistic particle acceleration
that is of interest, e.g., in the context of auroral arcs and solar flares, and
relativistic particle energization that is relevant, e.g., in the context of
active galactic nuclei.Comment: Physics of Plasmas, in prin
Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
We consider the random-bond +- J Ising model on a square lattice as a
function of the temperature T and of the disorder parameter p (p=1 corresponds
to the pure Ising model). We investigate the critical behavior along the
paramagnetic-ferromagnetic transition line at low temperatures, below the
temperature of the multicritical Nishimori point at T*= 0.9527(1),
p*=0.89083(3). We present finite-size scaling analyses of Monte Carlo results
at two temperature values, T=0.645 and T=0.5. The results show that the
paramagnetic-ferromagnetic transition line is reentrant for T<T*, that the
transitions are continuous and controlled by a strong-disorder fixed point with
critical exponents nu=1.50(4) and eta=0.128(8), and beta = 0.095(5). This fixed
point is definitely different from the Ising fixed point controlling the
paramagnetic-ferromagnetic transitions for T>T*. Our results for the critical
exponents are consistent with the hyperscaling relation 2 beta/nu - eta = d - 2
= 0.Comment: 32 pages, added refs and a discussion on hyperscalin
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