179 research outputs found
Equilibrium of anchored interfaces with quenched disordered growth
The roughening behavior of a one-dimensional interface fluctuating under
quenched disorder growth is examined while keeping an anchored boundary. The
latter introduces detailed balance conditions which allows for a thorough
analysis of equilibrium aspects at both macroscopic and microscopic scales. It
is found that the interface roughens linearly with the substrate size only in
the vicinity of special disorder realizations. Otherwise, it remains stiff and
tilted.Comment: 6 pages, 3 postscript figure
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
On the Scale-Invariant Distribution of the Diffusion Coefficient for Classical Particles Diffusing in Disordered Media.-
The scaling form of the whole distribution P(D) of the random diffusion
coefficient D(x) in a model of classically diffusing particles is investigated.
The renormalization group approach above the lower critical dimension d=0 is
applied to the distribution P(D) using the n-replica approach. In the annealed
approximation (n=1), the inverse gaussian distribution is found to be the
stable one under rescaling. This identification is made based on symmetry
arguments and subtle relations between this model and that of fluc- tuating
interfaces studied by Wallace and Zia. The renormalization-group flow for the
ratios between consecutive cumulants shows a regime of pure diffusion for small
disorder, in which P(D) goes to delta(D-), and a regime of strong disorder
where the cumulants grow infinitely large and the diffusion process is ill
defined. The boundary between these two regimes is associated with an unstable
fixed-point and a subdiffusive behavior: =Ct**(1-d/2). For the quenched
case (n goes to 0) we find that unphysical operators are generated raisng
doubts on the renormalizability of this model. Implications to other random
systems near their lower critical dimension are discussed.Comment: 21 pages, 1 fig. (not included) Use LaTex twic
Equilibrium roughening transition in a 1D modified sine-Gordon model
We present a modified version of the one-dimensional sine-Gordon that
exhibits a thermodynamic, roughening phase transition, in analogy with the 2D
usual sine-Gordon model. The model is suited to study the crystalline growth
over an impenetrable substrate and to describe the wetting transition of a
liquid that forms layers. We use the transfer integral technique to write down
the pseudo-Schr\"odinger equation for the model, which allows to obtain some
analytical insight, and to compute numerically the free energy from the exact
transfer operator. We compare the results with Monte Carlo simulations of the
model, finding a perfect agreement between both procedures. We thus establish
that the model shows a phase transition between a low temperature flat phase
and a high temperature rough one. The fact that the model is one dimensional
and that it has a true phase transition makes it an ideal framework for further
studies of roughening phase transitions.Comment: 11 pages, 13 figures. Accepted for publication in Physical Review
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
Non-perturbative phenomena in the three-dimensional random field Ising model
The systematic approach for the calculations of the non-perturbative
contributions to the free energy in the ferromagnetic phase of the random field
Ising model is developed. It is demonstrated that such contributions appear due
to localized in space instanton-like excitations. It is shown that away from
the critical region such instanton solutions are described by the set of the
mean-field saddle-point equations for the replica vector order parameter, and
these equations can be formally reduced to the only saddle-point equation of
the pure system in dimensions (D-2). In the marginal case, D=3, the
corresponding non-analytic contribution is computed explicitly. Nature of the
phase transition in the three-dimensional random field Ising model is
discussed.Comment: 12 page
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
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
Ground-State Roughness of the Disordered Substrate and Flux Line in d=2
We apply optimization algorithms to the problem of finding ground states for
crystalline surfaces and flux lines arrays in presence of disorder. The
algorithms provide ground states in polynomial time, which provides for a more
precise study of the interface widths than from Monte Carlo simulations at
finite temperature. Using systems up to size , with a minimum of
realizations at each size, we find very strong evidence for a
super-rough state at low temperatures.Comment: 10 pages, 3 PS figures, to appear in PR
Super-roughening as a disorder-dominated flat phase
We study the phenomenon of super-roughening found on surfaces growing on
disordered substrates. We consider a one-dimensional version of the problem for
which the pure, ordered model exhibits a roughening phase transition. Extensive
numerical simulations combined with analytical approximations indicate that
super-roughening is a regime of asymptotically flat surfaces with non-trivial,
rough short-scale features arising from the competition between surface tension
and disorder. Based on this evidence and on previous simulations of the
two-dimensional Random sine-Gordon model [Sanchez et al., Phys. Rev. E 62, 3219
(2000)], we argue that this scenario is general and explains equally well the
hitherto poorly understood two-dimensional case.Comment: 7 pages, 4 figures. Accepted for publication in Europhysics Letter
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