8,136 research outputs found
Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey
We consider a system of three random walkers (a `cheetah' surrounded by two
`antelopes') diffusing in one dimension. The cheetah and the antelopes diffuse,
but the antelopes experience in addition a deterministic relative drift
velocity, away from the cheetah, proportional to their distance from the
cheetah, such that they tend to move away from the cheetah with increasing
time. Using the backward Fokker-Planck equation we calculate, as a function of
their initial separations, the probability that the cheetah has caught neither
antelope after infinite time.Comment: 5 page
Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results
We consider the pair correlation functions of both the order parameter field
and its square for phase ordering in the model with nonconserved order
parameter, in spatial dimension and spin dimension .
We calculate, in the scaling limit, the exact short-distance singularities of
these correlation functions and compare these predictions to numerical
simulations. Our results suggest that the scaling hypothesis does not hold for
the model. Figures (23) are available on request - email
[email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2
The de Almeida-Thouless line in vector spin glasses
We consider the infinite-range spin glass in which the spins have m > 1
components (a vector spin glass). Applying a magnetic field which is random in
direction, there is an Almeida Thouless (AT) line below which the "replica
symmetric" solution is unstable, just as for the Ising (m=1) case. We calculate
the location of this AT line for Gaussian random fields for arbitrary m, and
verify our results by numerical simulations for m = 3$.Comment: 19 pages, 4 eps figure
Langevin Equation for the Density of a System of Interacting Langevin Processes
We present a simple derivation of the stochastic equation obeyed by the
density function for a system of Langevin processes interacting via a pairwise
potential. The resulting equation is considerably different from the
phenomenological equations usually used to describe the dynamics of non
conserved (Model A) and conserved (Model B) particle systems. The major feature
is that the spatial white noise for this system appears not additively but
multiplicatively. This simply expresses the fact that the density cannot
fluctuate in regions devoid of particles. The steady state for the density
function may however still be recovered formally as a functional integral over
the coursed grained free energy of the system as in Models A and B.Comment: 6 pages, latex, no figure
Non-Markovian Persistence at the PC point of a 1d non-equilibrium kinetic Ising model
One-dimensional non-equilibrium kinetic Ising models evolving under the
competing effect of spin flips at zero temperature and nearest neighbour spin
exchanges exhibiting a parity-conserving (PC) phase transition on the level of
kinks are investigated here numerically from the point of view of the
underlying spin system. The dynamical persistency exponent and the
exponent characterising the two-time autocorrelation function of the
total magnetization under non-equilibrium conditions are reported. It is found
that the PC transition has strong effect: the process becomes non-Markovian and
the above exponents exhibit drastic changes as compared to the Glauber-Ising
case.Comment: 6 pages, Latex, postscript figures include
Singlet-Triplet Excitations in the Unconventional Spin-Peierls System TiOBr
We have performed time-of-flight neutron scattering measurements on powder
samples of the unconventional spin-Peierls compound TiOBr using the
fine-resolution Fermi chopper spectrometer (SEQUOIA) at the SNS. These
measurements reveal two branches of magnetic excitations within the
commensurate and incommensurate spin-Peierls phases, which we associate with n
= 1 and n = 2 triplet excitations out of the singlet ground state. These
measurements represent the first direct measure of the singlet-triplet energy
gap in TiOBr, which is determined to be Eg = 21.2 +/- 1.0 meV.Comment: 5 pages, 4 figures, submitted for publicatio
Absence of aging in the remanent magnetization in Migdal-Kadanoff spin glasses
We study the non-equilibrium behavior of three-dimensional spin glasses in
the Migdal-Kadanoff approximation, that is on a hierarchical lattice. In this
approximation the model has an unique ground state and equilibrium properties
correctly described by the droplet model. Extensive numerical simulations show
that this model lacks aging in the remanent magnetization as well as a maximum
in the magnetic viscosity in disagreement with experiments as well as with
numerical studies of the Edwards-Anderson model. This result strongly limits
the validity of the droplet model (at least in its simplest form) as a good
model for real spin glasses.Comment: 4 pages and 3 figures. References update
Growth Laws for Phase Ordering
We determine the characteristic length scale, , in phase ordering
kinetics for both scalar and vector fields, with either short- or long-range
interactions, and with or without conservation laws. We obtain
consistently by comparing the global rate of energy change to the energy
dissipation from the local evolution of the order parameter. We derive growth
laws for O(n) models, and our results can be applied to other systems with
similar defect structures.Comment: 12 pages, LaTeX, second tr
Slow Logarithmic Decay of Magnetization in the Zero Temperature Dynamics of an Ising Spin Chain: Analogy to Granular Compaction
We study the zero temperature coarsening dynamics in an Ising chain in
presence of a dynamically induced field that favors locally the `-' phase
compared to the `+' phase. At late times, while the `+' domains still coarsen
as , the `-' domains coarsen slightly faster as . As
a result, at late times, the magnetization decays slowly as, . We establish this behavior both analytically within an
independent interval approximation (IIA) and numerically. In the zero volume
fraction limit of the `+' phase, we argue that the IIA becomes asymptotically
exact. Our model can be alternately viewed as a simple Ising model for granular
compaction. At late times in our model, the system decays into a fully compact
state (where all spins are `-') in a slow logarithmic manner , a fact that has been observed in recent experiments on granular systems.Comment: 4 pages Revtex, 3 eps figures, supersedes cond-mat/000221
Correlated random fields in dielectric and spin glasses
Both orientational glasses and dipolar glasses possess an intrinsic random
field, coming from the volume difference between impurity and host ions. We
show this suppresses the glass transition, causing instead a crossover to the
low phase. Moreover the random field is correlated with the inter-impurity
interactions, and has a broad distribution. This leads to a peculiar variant of
the Imry-Ma mechanism, with 'domains' of impurities oriented by a few frozen
pairs. These domains are small: predictions of domain size are given for
specific systems, and their possible experimental verification is outlined. In
magnetic glasses in zero field the glass transition survives, because the
random fields are disallowed by time-reversal symmetry; applying a magnetic
field then generates random fields, and suppresses the spin glass transition.Comment: minor modifications, final versio
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