46 research outputs found
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
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
Reversal-Field Memory in the Hysteresis of Spin Glasses
We report a novel singularity in the hysteresis of spin glasses, the
reversal-field memory effect, which creates a non-analyticity in the
magnetization curves at a particular point related to the history of the
sample. The origin of the effect is due to the existence of a macroscopic
number of "symmetric clusters" of spins associated with a local spin-reversal
symmetry of the Hamiltonian. We use First Order Reversal Curve (FORC) diagrams
to characterize the effect and compare to experimental results on thin magnetic
films. We contrast our results on spin glasses to random magnets and show that
the FORC technique is an effective "magnetic fingerprinting" tool.Comment: 4 pages, 6 figure
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
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
Ground-state energy and entropy of the two-dimensional Edwards-Anderson spin-glass model with different bond distributions
We study the two-dimensional Edwards-Anderson spin-glass model using a
parallel tempering Monte Carlo algorithm. The ground-state energy and entropy
are calculated for different bond distributions. In particular, the entropy is
obtained by using a thermodynamic integration technique and an appropriate
reference state, which is determined with the method of high-temperature
expansion. This strategy provide accurate values of this quantity for
finite-size lattices. By extrapolating to the thermodynamic limit, the
ground-state energy and entropy of the different versions of the spin-glass
model are determined.Comment: 18 pages, 5 figure
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
Phase diagram of a Disordered Boson Hubbard Model in Two Dimensions
We study the zero-temperature phase transition of a two-dimensional
disordered boson Hubbard model. The phase diagram of this model is constructed
in terms of the disorder strength and the chemical potential. Via quantum Monte
Carlo simulations, we find a multicritical line separating the weak-disorder
regime, where a random potential is irrelevant, from the strong-disorder
regime. In the weak-disorder regime, the Mott-insulator-to-superfluid
transition occurs, while, in the strong-disorder regime, the
Bose-glass-to-superfluid transition occurs. On the multicritical line, the
insulator-to-superfluid transition has the dynamical critical exponent and the correlation length critical exponent ,
that are different from the values for the transitions off the line. We suggest
that the proliferation of the particle-hole pairs screens out the weak disorder
effects.Comment: 4 pages, 4 figures, to be published in PR
The ground state energy of the Edwards-Anderson spin glass model with a parallel tempering Monte Carlo algorithm
We study the efficiency of parallel tempering Monte Carlo technique for
calculating true ground states of the Edwards-Anderson spin glass model.
Bimodal and Gaussian bond distributions were considered in two and
three-dimensional lattices. By a systematic analysis we find a simple formula
to estimate the values of the parameters needed in the algorithm to find the GS
with a fixed average probability. We also study the performance of the
algorithm for single samples, quantifying the difference between samples where
the GS is hard, or easy, to find. The GS energies we obtain are in good
agreement with the values found in the literature. Our results show that the
performance of the parallel tempering technique is comparable to more powerful
heuristics developed to find the ground state of Ising spin glass systems.Comment: 30 pages, 17 figures. A new section added. Accepted for publication
in Physica