107 research outputs found
Magnetic Properties of the Metamagnet Ising Model in a three-dimensional Lattice in a Random and Uniform Field
By employing the Monte Carlo technique we study the behavior of Metamagnet
Ising Model in a random field. The phase diagram is obtained by using the
algorithm of Glaubr in a cubic lattice of linear size with values ranging
from 16 to 42 and with periodic boundary conditions.Comment: 4 pages, 6 figure
Magneto-Conductance Anisotropy and Interference Effects in Variable Range Hopping
We investigate the magneto-conductance (MC) anisotropy in the variable range
hopping regime, caused by quantum interference effects in three dimensions.
When no spin-orbit scattering is included, there is an increase in the
localization length (as in two dimensions), producing a large positive MC. By
contrast, with spin-orbit scattering present, there is no change in the
localization length, and only a small increase in the overall tunneling
amplitude. The numerical data for small magnetic fields , and hopping
lengths , can be collapsed by using scaling variables , and
in the perpendicular and parallel field orientations
respectively. This is in agreement with the flux through a `cigar'--shaped
region with a diffusive transverse dimension proportional to . If a
single hop dominates the conductivity of the sample, this leads to a
characteristic orientational `finger print' for the MC anisotropy. However, we
estimate that many hops contribute to conductivity of typical samples, and thus
averaging over critical hop orientations renders the bulk sample isotropic, as
seen experimentally. Anisotropy appears for thin films, when the length of the
hop is comparable to the thickness. The hops are then restricted to align with
the sample plane, leading to different MC behaviors parallel and perpendicular
to it, even after averaging over many hops. We predict the variations of such
anisotropy with both the hop size and the magnetic field strength. An
orientational bias produced by strong electric fields will also lead to MC
anisotropy.Comment: 24 pages, RevTex, 9 postscript figures uuencoded Submitted to PR
Quantum site percolation on amenable graphs
We consider the quantum site percolation model on graphs with an amenable
group action. It consists of a random family of Hamiltonians. Basic spectral
properties of these operators are derived: non-randomness of the spectrum and
its components, existence of an self-averaging integrated density of states and
an associated trace-formula.Comment: 10 pages, LaTeX 2e, to appear in "Applied Mathematics and Scientific
Computing", Brijuni, June 23-27, 2003. by Kluwer publisher
Au-Ag template stripped pattern for scanning probe investigations of DNA arrays produced by Dip Pen Nanolithography
We report on DNA arrays produced by Dip Pen Nanolithography (DPN) on a novel
Au-Ag micro patterned template stripped surface. DNA arrays have been
investigated by atomic force microscopy (AFM) and scanning tunnelling
microscopy (STM) showing that the patterned template stripped substrate enables
easy retrieval of the DPN-functionalized zone with a standard optical
microscope permitting a multi-instrument and multi-technique local detection
and analysis. Moreover the smooth surface of the Au squares (abput 5-10
angstrom roughness) allows to be sensitive to the hybridization of the
oligonucleotide array with label-free target DNA. Our Au-Ag substrates,
combining the retrieving capabilities of the patterned surface with the
smoothness of the template stripped technique, are candidates for the
investigation of DPN nanostructures and for the development of label free
detection methods for DNA nanoarrays based on the use of scanning probes.Comment: Langmuir (accepted
Identity of the universal repulsive-core singularity with Yang-Lee edge criticality
Lattice and continuum fluid models with repulsive-core interactions typically
display a dominant, critical-type singularity on the real, negative activity
axis. Lai and Fisher recently suggested, mainly on numerical grounds, that this
repulsive-core singularity is universal and in the same class as the Yang-Lee
edge singularities, which arise above criticality at complex activities with
positive real part. A general analytic demonstration of this identification is
presented here using a field-theory approach with separate representation of
the repulsive and attractive parts of the pair interactions.Comment: 6 pages, 3 figure
Glassy Roughness of a Crystalline Surface Upon a Disordered Substrate
The discrete Gaussian model for the surface of a crystal deposited on a
disordered substrate is studied by Monte Carlo simulations. A continuous
transition is found from a phase with a thermally-induced roughness to a glassy
one in which the roughness is driven by the disorder. The behavior of the
height-height correlations is consistent with the one-step replica symmetry
broken solution of the variational approximation. The results differ from the
renormalization group predictions and from recent simulations of a 2D
vortex-glass model which belongs to the same universality class.Comment: 12 pages (RevTeX) & 3 figures (PS) uuencode
Roughness Scaling in Cyclical Surface Growth
The scaling behavior of cyclical growth (e.g. cycles of alternating
deposition and desorption primary processes) is investigated theoretically and
probed experimentally. The scaling approach to kinetic roughening is
generalized to cyclical processes by substituting the time by the number of
cycles . The roughness is predicted to grow as where is
the cyclical growth exponent. The roughness saturates to a value which scales
with the system size as , where is the cyclical
roughness exponent. The relations between the cyclical exponents and the
corresponding exponents of the primary processes are studied. Exact relations
are found for cycles composed of primary linear processes. An approximate
renormalization group approach is introduced to analyze non-linear effects in
the primary processes. The analytical results are backed by extensive numerical
simulations of different pairs of primary processes, both linear and
non-linear. Experimentally, silver surfaces are grown by a cyclical process
composed of electrodeposition followed by 50% electrodissolution. The roughness
is found to increase as a power-law of , consistent with the scaling
behavior anticipated theoretically. Potential applications of cyclical scaling
include accelerated testing of rechargeable batteries, and improved
chemotherapeutic treatment of cancerous tumors
Directed paths on hierarchical lattices with random sign weights
We study sums of directed paths on a hierarchical lattice where each bond has
either a positive or negative sign with a probability . Such path sums
have been used to model interference effects by hopping electrons in the
strongly localized regime. The advantage of hierarchical lattices is that they
include path crossings, ignored by mean field approaches, while still
permitting analytical treatment. Here, we perform a scaling analysis of the
controversial ``sign transition'' using Monte Carlo sampling, and conclude that
the transition exists and is second order. Furthermore, we make use of exact
moment recursion relations to find that the moments always determine,
uniquely, the probability distribution $P(J)$. We also derive, exactly, the
moment behavior as a function of $p$ in the thermodynamic limit. Extrapolations
($n\to 0$) to obtain for odd and even moments yield a new signal for
the transition that coincides with Monte Carlo simulations. Analysis of high
moments yield interesting ``solitonic'' structures that propagate as a function
of . Finally, we derive the exact probability distribution for path sums
up to length L=64 for all sign probabilities.Comment: 20 pages, 12 figure
Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. IV. Chromatic polynomial with cyclic boundary conditions
We study the chromatic polynomial P_G(q) for m \times n square- and
triangular-lattice strips of widths 2\leq m \leq 8 with cyclic boundary
conditions. This polynomial gives the zero-temperature limit of the partition
function for the antiferromagnetic q-state Potts model defined on the lattice
G. We show how to construct the transfer matrix in the Fortuin--Kasteleyn
representation for such lattices and obtain the accumulation sets of chromatic
zeros in the complex q-plane in the limit n\to\infty. We find that the
different phases that appear in this model can be characterized by a
topological parameter. We also compute the bulk and surface free energies and
the central charge.Comment: 55 pages (LaTeX2e). Includes tex file, three sty files, and 22
Postscript figures. Also included are Mathematica files transfer4_sq.m and
transfer4_tri.m. Journal versio
Spin Transport in Two Dimensional Hopping Systems
A two dimensional hopping system with Rashba spin-orbit interaction is
considered. Our main interest is concerned with the evolution of the spin
degree of freedom of the electrons. We derive the rate equations governing the
evolution of the charge density and spin polarization of this system in the
Markovian limit in one-particle approximation. If only two-site hopping events
are taken into account, the evolution of the charge density and of the spin
polarization is found to be decoupled. A critical electric field is found,
above which oscillations are superimposed on the temporal decay of the total
polarization. A coupling between charge density and spin polarization occurs on
the level of three-site hopping events. The coupling terms are identified as
the anomalous Hall effect and the recently proposed spin Hall effect. Thus, an
unpolarized charge current through a sheet of finite width leads to a
transversal spin accumulation in our model system.Comment: 15 pages, 3 figure
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