34 research outputs found
Mean Field Theory of the Localization Transition
A mean field theory of the localization transition for bosonic systems is
developed. Localization is shown to be sensitive to the distribution of the
random site energies. It occurs in the presence of a triangular distribution,
but not a uniform one. The inverse participation ratio, the single site Green's
function, the superfluid order parameter and the corresponding susceptibility
are calculated, and the appropriate exponents determined. All of these
quantities indicate the presence of a new phase, which can be identified as the
{\it Bose-glass}.Comment: 4 pages, Revtex, 2 figures appende
Disorder Averaging and Finite Size Scaling
We propose a new picture of the renormalization group (RG) approach in the
presence of disorder, which considers the RG trajectories of each random sample
(realization) separately instead of the usual renormalization of the averaged
free energy. The main consequence of the theory is that the average over
randomness has to be taken after finding the critical point of each
realization. To demonstrate these concepts, we study the finite-size scaling
properties of the two-dimensional random-bond Ising model. We find that most of
the previously observed finite-size corrections are due to the sample-to-sample
fluctuation of the critical temperature and scaling is more adequate in terms
of the new scaling variables.Comment: 4 pages, 6 figures include
Direct Mott Insulator-to-Superfluid Transition in the Presence of Disorder
We introduce a new renormalization group theory to examine the quantum phase
transitions upon exiting the insulating phase of a disordered, strongly
interacting boson system. For weak disorder we find a direct transition from
this Mott insulator to the Superfluid phase. In d > 4 a finite region around
the particle-hole symmetric point supports this direct transition, whereas for
2=< d <4 perturbative arguments suggest that the direct transition survives
only precisely at commensurate filling. For strong disorder the renormalization
trajectories pass next to two fixed points, describing a pair of distinct
transitions; first from the Mott insulator to the Bose glass, and then from the
Bose glass to the Superfluid. The latter fixed point possesses statistical
particle-hole symmetry and a dynamical exponent z, equal to the dimension d.Comment: 4 pages, Latex, submitted to Physical Review Letter
Tejsavasan erjesztett savó alapú ital kifejlesztésének membrán-szeparációs és mikrobiológiai alapjai
Revisiting the Theory of Finite Size Scaling in Disordered Systems: \nu Can Be Less Than 2/d
For phase transitions in disordered systems, an exact theorem provides a
bound on the finite size correlation length exponent: \nu_{FS}<= 2/d. It is
believed that the true critical exponent \nu of a disorder induced phase
transition satisfies the same bound. We argue that in disordered systems the
standard averaging introduces a noise, and a corresponding new diverging length
scale, characterized by \nu_{FS}=2/d. This length scale, however, is
independent of the system's own correlation length \xi. Therefore \nu can be
less than 2/d. We illustrate these ideas on two exact examples, with \nu < 2/d.
We propose a new method of disorder averaging, which achieves a remarkable
noise reduction, and thus is able to capture the true exponents.Comment: 4 pages, Latex, one figure in .eps forma
Self-organized criticality in the hysteresis of the Sherrington - Kirkpatrick model
We study hysteretic phenomena in random ferromagnets. We argue that the angle
dependent magnetostatic (dipolar) terms introduce frustration and long range
interactions in these systems. This makes it plausible that the Sherrington -
Kirkpatrick model may be able to capture some of the relevant physics of these
systems. We use scaling arguments, replica calculations and large scale
numerical simulations to characterize the hysteresis of the zero temperature SK
model. By constructing the distribution functions of the avalanche sizes,
magnetization jumps and local fields, we conclude that the system exhibits
self-organized criticality everywhere on the hysteresis loop.Comment: 4 pages, 4 eps figure
Hysteretic Optimization
We propose a new optimization method based on a demagnetization procedure
well known in magnetism. We show how this procedure can be applied as a general
tool to search for optimal solutions in any system where the configuration
space is endowed with a suitable `distance'. We test the new algorithm on
frustrated magnetic models and the traveling salesman problem. We find that the
new method successfully competes with similar basic algorithms such as
simulated annealing.Comment: 5 pages, 5 figure
On the statistical mechanics of prion diseases
We simulate a two-dimensional, lattice based, protein-level statistical
mechanical model for prion diseases (e.g., Mad Cow disease) with concommitant
prion protein misfolding and aggregation. Our simulations lead us to the
hypothesis that the observed broad incubation time distribution in
epidemiological data reflect fluctuation dominated growth seeded by a few
nanometer scale aggregates, while much narrower incubation time distributions
for innoculated lab animals arise from statistical self averaging. We model
`species barriers' to prion infection and assess a related treatment protocol.Comment: 5 Pages, 3 eps figures (submitted to Physical Review Letters
Finite-Size Scaling Study of the Surface and Bulk Critical Behavior in the Random-Bond 8-state Potts Model
The self-dual random-bond eight-state Potts model is studied numerically
through large-scale Monte Carlo simulations using the Swendsen-Wang cluster
flipping algorithm. We compute bulk and surface order parameters and
susceptibilities and deduce the corresponding critical exponents at the random
fixed point using standard finite-size scaling techniques. The scaling laws are
suitably satisfied. We find that a belonging of the model to the 2D Ising model
universality class can be conclusively ruled out, and the dimensions of the
relevant bulk and surface scaling fields are found to take the values
, , , to be compared to their Ising values:
15/8, 1, and 1/2.Comment: LaTeX file with Revtex, 4 pages, 4 eps figures, to appear in Phys.
Rev. Let
Critical behavior at superconductor-insulator phase transitions near one dimension
I argue that the system of interacting bosons at zero temperature and in
random external potential possesses a simple critical point which describes the
proliferation of disorder-induced topological defects in the superfluid ground
state, and which is located at weak disorder close to and above one dimension.
This makes it possible to address the critical behavior at the superfluid-Bose
glass transition in dirty boson systems by expanding around the lower critical
dimension d=1. Within the formulated renormalization procedure near d=1 the
dynamical critical exponent is obtained exactly and the correlation length
exponent is calculated as a Laurent series in the parameter \sqrt{\epsilon},
with \epsilon=d-1: z=d, \nu=1/\sqrt{3\epsilon} for the short range, and z=1,
\nu=\sqrt{2/3\epsilon}, for the long-range Coulomb interaction between bosons.
The identified critical point should be stable against the residual
perturbations in the effective action for the superfluid, at least in
dimensions 1\leq d \leq 2, for both short-range and Coulomb interactions. For
the superfluid-Mott insulator transition in the system in a periodic potential
and at a commensurate density of bosons I find \nu=(1/2\sqrt{\epsilon})+
1/4+O(\sqrt{\epsilon}), which yields a result reasonably close to the known XY
critical exponent in d=2+1. The critical behavior of the superfluid density,
phonon velocity and the compressibility in the system with the short-range
interactions is discussed.Comment: 23 pages, 1 Postscript figure, LaTe