28,620 research outputs found
Persistence and the Random Bond Ising Model in Two Dimensions
We study the zero-temperature persistence phenomenon in the random bond Ising model on a square lattice via extensive numerical simulations. We find
strong evidence for ` blocking\rq regardless of the amount disorder present in
the system. The fraction of spins which {\it never} flips displays interesting
non-monotonic, double-humped behaviour as the concentration of ferromagnetic
bonds is varied from zero to one. The peak is identified with the onset of
the zero-temperature spin glass transition in the model. The residual
persistence is found to decay algebraically and the persistence exponent
over the range . Our results are
completely consistent with the result of Gandolfi, Newman and Stein for
infinite systems that this model has ` mixed\rq behaviour, namely positive
fractions of spins that flip finitely and infinitely often, respectively.
[Gandolfi, Newman and Stein, Commun. Math. Phys. {\bf 214} 373, (2000).]Comment: 9 pages, 5 figure
Persistence in a Random Bond Ising Model of Socio-Econo Dynamics
We study the persistence phenomenon in a socio-econo dynamics model using
computer simulations at a finite temperature on hypercubic lattices in
dimensions up to 5. The model includes a ` social\rq local field which contains
the magnetization at time . The nearest neighbour quenched interactions are
drawn from a binary distribution which is a function of the bond concentration,
. The decay of the persistence probability in the model depends on both the
spatial dimension and . We find no evidence of ` blocking\rq in this model.
We also discuss the implications of our results for possible applications in
the social and economic fields. It is suggested that the absence, or otherwise,
of blocking could be used as a criterion to decide on the validity of a given
model in different scenarios.Comment: 11 pages, 4 figure
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Dynamic Costly State Verification with Repeated Loans: a two-period analysis
We derive the optimal contract in a two period costly state verification model with repeated loans, where in each period, the borrower invests in an identical project. We allow the borrower to switch lenders at the end of the first period. We show that while the second period optimal contract continues to be a standard debt contract, the optimal contract for the first project need not be. Regardless of the form of the first period contract, there is less monitoring in the first period and total monitoring costs are strictly lower, relative to a sequence of short term contracts. We illustrate our results assuming a uniform distribution for firm revenue and fixed monitoring costs. In particular, we show that either there is no monitoring in the first period or maximum possible amount consistent with the outside option is collected in the second period
Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness
The activation gaps for fractional quantum Hall states at filling fractions
are computed for heterojunction, square quantum well, as well as
parabolic quantum well geometries, using an interaction potential calculated
from a self-consistent electronic structure calculation in the local density
approximation. The finite thickness is estimated to make 30% correction
to the gap in the heterojunction geometry for typical parameters, which
accounts for roughly half of the discrepancy between the experiment and
theoretical gaps computed for a pure two dimensional system. Certain model
interactions are also considered. It is found that the activation energies
behave qualitatively differently depending on whether the interaction is of
longer or shorter range than the Coulomb interaction; there are indications
that fractional Hall states close to the Fermi sea are destabilized for the
latter.Comment: 32 pages, 13 figure
Exact solution of a model of time-dependent evolutionary dynamics in a rugged fitness landscape
A simplified form of the time dependent evolutionary dynamics of a
quasispecies model with a rugged fitness landscape is solved via a mapping onto
a random flux model whose asymptotic behavior can be described in terms of a
random walk. The statistics of the number of changes of the dominant genotype
from a finite set of genotypes are exactly obtained confirming existing
conjectures based on numerics.Comment: 5 pages RevTex 2 figures .ep
Evolutionary dynamics of the most populated genotype on rugged fitness landscapes
We consider an asexual population evolving on rugged fitness landscapes which
are defined on the multi-dimensional genotypic space and have many local
optima. We track the most populated genotype as it changes when the population
jumps from a fitness peak to a better one during the process of adaptation.
This is done using the dynamics of the shell model which is a simplified
version of the quasispecies model for infinite populations and standard
Wright-Fisher dynamics for large finite populations. We show that the
population fraction of a genotype obtained within the quasispecies model and
the shell model match for fit genotypes and at short times, but the dynamics of
the two models are identical for questions related to the most populated
genotype. We calculate exactly several properties of the jumps in infinite
populations some of which were obtained numerically in previous works. We also
present our preliminary simulation results for finite populations. In
particular, we measure the jump distribution in time and find that it decays as
as in the quasispecies problem.Comment: Minor changes. To appear in Phys Rev
Persistence in the Zero-Temperature Dynamics of the Diluted Ising Ferromagnet in Two Dimensions
The non-equilibrium dynamics of the strongly diluted random-bond Ising model
in two-dimensions (2d) is investigated numerically.
The persistence probability, P(t), of spins which do not flip by time t is
found to decay to a non-zero, dilution-dependent, value . We find
that decays exponentially to zero at large times.
Furthermore, the fraction of spins which never flip is a monotonically
increasing function over the range of bond-dilution considered. Our findings,
which are consistent with a recent result of Newman and Stein, suggest that
persistence in disordered and pure systems falls into different classes.
Furthermore, its behaviour would also appear to depend crucially on the
strength of the dilution present.Comment: some minor changes to the text, one additional referenc
Tests of Gravity from Imaging and Spectroscopic Surveys
Tests of gravity on large-scales in the universe can be made using both
imaging and spectroscopic surveys. The former allow for measurements of weak
lensing, galaxy clustering and cross-correlations such as the ISW effect. The
latter probe galaxy dynamics through redshift space distortions. We use a set
of basic observables, namely lensing power spectra, galaxy-lensing and
galaxy-velocity cross-spectra in multiple redshift bins (including their
covariances), to estimate the ability of upcoming surveys to test gravity
theories. We use a two-parameter description of gravity that allows for the
Poisson equation and the ratio of metric potentials to depart from general
relativity. We find that the combination of imaging and spectroscopic
observables is essential in making robust tests of gravity theories. The range
of scales and redshifts best probed by upcoming surveys is discussed. We also
compare our parametrization to others used in the literature, in particular the
gamma parameter modification of the growth factor.Comment: 18 pages, 10 figures, to be submitte
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