9,819 research outputs found
Random and aperiodic quantum spin chains: A comparative study
According to the Harris-Luck criterion the relevance of a fluctuating
interaction at the critical point is connected to the value of the fluctuation
exponent omega. Here we consider different types of relevant fluctuations in
the quantum Ising chain and investigate the universality class of the models.
At the critical point the random and aperiodic systems behave similarly, due to
the same type of extreme broad distribution of the energy scales at low
energies. The critical exponents of some averaged quantities are found to be a
universal function of omega, but some others do depend on other parameters of
the distribution of the couplings. In the off-critical region there is an
important difference between the two systems: there are no Griffiths
singularities in aperiodic models.Comment: 4 pages RevTeX, 2 eps-figures include
Comparative study of the critical behavior in one-dimensional random and aperiodic environments
We consider cooperative processes (quantum spin chains and random walks) in
one-dimensional fluctuating random and aperiodic environments characterized by
fluctuating exponents omega>0. At the critical point the random and aperiodic
systems scale essentially anisotropically in a similar fashion: length (L) and
time (t) scales are related as t ~ log^{1/omega}. Also some critical exponents,
characterizing the singularities of average quantities, are found to be
universal functions of omega, whereas some others do depend on details of the
distribution of the disorder. In the off-critical region there is an important
difference between the two types of environments: in aperiodic systems there
are no extra (Griffiths)-singularities.Comment: 13 pages RevTeX, 10 eps-figures include
Effect of surface nanostructure on temperature programmed reaction spectroscopy: First-principles kinetic Monte Carlo simulations of CO oxidation at RuO2(110)
Using the catalytic CO oxidation at RuO2(110) as a showcase, we employ
first-principles kinetic Monte Carlo simulations to illustrate the intricate
effects on temperature programmed reaction spectroscopy data brought about by
the mere correlations between the locations of the active sites at a
nanostructured surface. Even in the absence of lateral interactions, this
nanostructure alone can cause inhomogeneities that cannot be grasped by
prevalent mean-field data analysis procedures, which thus lead to wrong
conclusions on the reactivity of the different surface species.Comment: 4 pages including 3 figures; related publications can be found at
http://www.fhi-berlin.mpg.de/th/th.htm
Chaos in the Random Field Ising Model
The sensitivity of the random field Ising model to small random perturbations
of the quenched disorder is studied via exact ground states obtained with a
maximum-flow algorithm. In one and two space dimensions we find a mild form of
chaos, meaning that the overlap of the old, unperturbed ground state and the
new one is smaller than one, but extensive. In three dimensions the
rearrangements are marginal (concentrated in the well defined domain walls).
Implications for finite temperature variations and experiments are discussed.Comment: 4 pages RevTeX, 6 eps-figures include
Three-dimensional flows in slowly-varying planar geometries
We consider laminar flow in channels constrained geometrically to remain
between two parallel planes; this geometry is typical of microchannels obtained
with a single step by current microfabrication techniques. For pressure-driven
Stokes flow in this geometry and assuming that the channel dimensions change
slowly in the streamwise direction, we show that the velocity component
perpendicular to the constraint plane cannot be zero unless the channel has
both constant curvature and constant cross-sectional width. This result implies
that it is, in principle, possible to design "planar mixers", i.e. passive
mixers for channels that are constrained to lie in a flat layer using only
streamwise variations of their in-plane dimensions. Numerical results are
presented for the case of a channel with sinusoidally varying width
Path integral Monte Carlo study of the interacting quantum double-well model: Quantum phase transition and phase diagram
The discrete time path integral Monte Carlo (PIMC) with a one-particle
density matrix approximation is applied to study the quantum phase transition
in the coupled double-well chain. To improve the convergence properties, the
exact action for a single particle in a double well potential is used to
construct the many-particle action. The algorithm is applied to the interacting
quantum double-well chain for which the zero-temperature phase diagram is
determined. The quantum phase transition is studied via finite-size scaling and
the critical exponents are shown to be compatible with the classical
two-dimensional (2D) Ising universality class -- not only in the order-disorder
limit (deep potential wells) but also in the displacive regime (shallow
potential wells).Comment: 17 pages, 7 figures; Accepted for publication in Phys. Rev.
Critical Exponents of the Three Dimensional Random Field Ising Model
The phase transition of the three--dimensional random field Ising model with
a discrete () field distribution is investigated by extensive Monte
Carlo simulations. Values of the critical exponents for the correlation length,
specific heat, susceptibility, disconnected susceptibility and magnetization
are determined simultaneously via finite size scaling. While the exponents for
the magnetization and disconnected susceptibility are consistent with a first
order transition, the specific heat appears to saturate indicating no latent
heat. Sample to sample fluctuations of the susceptibilty are consistent with
the droplet picture for the transition.Comment: Revtex, 10 pages + 4 figures included as Latex files and 1 in
Postscrip
Fluctuation Dissipation Ratio in Three-Dimensional Spin Glasses
We present an analysis of the data on aging in the three-dimensional Edwards
Anderson spin glass model with nearest neighbor interactions, which is well
suited for the comparison with a recently developed dynamical mean field
theory. We measure the parameter describing the violation of the
relation among correlation and response function implied by the fluctuation
dissipation theorem.Comment: LaTeX 10 pages + 4 figures (appended as uuencoded compressed
tar-file), THP81-9
Phase Diagram and Storage Capacity of Sequence Processing Neural Networks
We solve the dynamics of Hopfield-type neural networks which store sequences
of patterns, close to saturation. The asymmetry of the interaction matrix in
such models leads to violation of detailed balance, ruling out an equilibrium
statistical mechanical analysis. Using generating functional methods we derive
exact closed equations for dynamical order parameters, viz. the sequence
overlap and correlation- and response functions, in the thermodynamic limit. We
calculate the time translation invariant solutions of these equations,
describing stationary limit-cycles, which leads to a phase diagram. The
effective retarded self-interaction usually appearing in symmetric models is
here found to vanish, which causes a significantly enlarged storage capacity of
, compared to \alpha_\c\sim 0.139 for Hopfield networks
storing static patterns. Our results are tested against extensive computer
simulations and excellent agreement is found.Comment: 17 pages Latex2e, 2 postscript figure
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