9,467 research outputs found
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
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
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
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
Flow correlated percolation during vascular network formation in tumors
A theoretical model based on the molecular interactions between a growing
tumor and a dynamically evolving blood vessel network describes the
transformation of the regular vasculature in normal tissues into a highly
inhomogeneous tumor specific capillary network. The emerging morphology,
characterized by the compartmentalization of the tumor into several regions
differing in vessel density, diameter and necrosis, is in accordance with
experimental data for human melanoma. Vessel collapse due to a combination of
severely reduced blood flow and solid stress exerted by the tumor, leads to a
correlated percolation process that is driven towards criticality by the
mechanism of hydrodynamic vessel stabilization.Comment: 4 pages, 3 figures (higher resolution at
http://www.uni-saarland.de/fak7/rieger/HOMEPAGE/flow.eps
Ground state properties of solid-on-solid models with disordered substrates
We study the glassy super-rough phase of a class of solid-on-solid models
with a disordered substrate in the limit of vanishing temperature by means of
exact ground states, which we determine with a newly developed minimum cost
flow algorithm. Results for the height-height correlation function are compared
with analytical and numerical predictions. The domain wall energy of a boundary
induced step grows logarithmically with system size, indicating the marginal
stability of the ground state, and the fractal dimension of the step is
estimated. The sensibility of the ground state with respect to infinitesimal
variations of the quenched disorder is analyzed.Comment: 4 pages RevTeX, 3 eps-figures include
Application of a minimum cost flow algorithm to the three-dimensional gauge glass model with screening
We study the three-dimensional gauge glass model in the limit of strong
screening by using a minimum cost flow algorithm, enabling us to obtain EXACT
ground states for systems of linear size L<=48. By calculating the domain-wall
energy, we obtain the stiffness exponent theta = -0.95+/-0.03, indicating the
absence of a finite temperature phase transition, and the thermal exponent
nu=1.05+/-0.03. We discuss the sensitivity of the ground state with respect to
small perturbations of the disorder and determine the overlap length, which is
characterized by the chaos exponent zeta=3.9+/-0.2, implying strong chaos.Comment: 4 pages RevTeX, 2 eps-figures include
Dislocations in the ground state of the solid-on-solid model on a disordered substrate
We investigate the effects of topological defects (dislocations) to the
ground state of the solid-on-solid (SOS) model on a simple cubic disordered
substrate utilizing the min-cost-flow algorithm from combinatorial
optimization. The dislocations are found to destabilize and destroy the elastic
phase, particularly when the defects are placed only in partially optimized
positions. For multi defect pairs their density decreases exponentially with
the vortex core energy. Their mean distance has a maximum depending on the
vortex core energy and system size, which gives a fractal dimension of . The maximal mean distances correspond to special vortex core
energies for which the scaling behavior of the density of dislocations change
from a pure exponential decay to a stretched one. Furthermore, an extra
introduced vortex pair is screened due to the disorder-induced defects and its
energy is linear in the vortex core energy.Comment: 6 pages RevTeX, eps figures include
Extended surface disorder in the quantum Ising chain
We consider random extended surface perturbations in the transverse field
Ising model decaying as a power of the distance from the surface towards a pure
bulk system. The decay may be linked either to the evolution of the couplings
or to their probabilities. Using scaling arguments, we develop a
relevance-irrelevance criterion for such perturbations. We study the
probability distribution of the surface magnetization, its average and typical
critical behaviour for marginal and relevant perturbations. According to
analytical results, the surface magnetization follows a log-normal distribution
and both the average and typical critical behaviours are characterized by
power-law singularities with continuously varying exponents in the marginal
case and essential singularities in the relevant case. For enhanced average
local couplings, the transition becomes first order with a nonvanishing
critical surface magnetization. This occurs above a positive threshold value of
the perturbation amplitude in the marginal case.Comment: 15 pages, 10 figures, Plain TeX. J. Phys. A (accepted
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