13,127 research outputs found
Zero area singularities in general relativity and inverse mean curvature flow
First we restate the definition of a Zero Area Singularity, recently
introduced by H. Bray. We then consider several definitions of mass for these
singularities. We use the Inverse Mean Curvature Flow to prove some new results
about the mass of a singularity, the ADM mass of the manifold, and the capacity
of the singularity.Comment: 13 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
A counter-example to a recent version of the Penrose conjecture
By considering suitable axially symmetric slices on the Kruskal spacetime, we
construct counterexamples to a recent version of the Penrose inequality in
terms of so-called generalized apparent horizons.Comment: 12 pages. Appendix added with technical details. To appear in
Classical and Quantum Gravit
Scaling Analysis of Domain-Wall Free-Energy in the Edwards-Anderson Ising Spin Glass in a Magnetic Field
The stability of the spin-glass phase against a magnetic field is studied in
the three and four dimensional Edwards-Anderson Ising spin glasses. Effective
couplings and effective fields associated with length scale L are measured by a
numerical domain-wall renormalization group method. The results obtained by
scaling analysis of the data strongly indicate the existence of a crossover
length beyond which the spin-glass order is destroyed by field H. The crossover
length well obeys a power law of H which diverges as H goes to zero but remains
finite for any non-zero H, implying that the spin-glass phase is absent even in
an infinitesimal field. These results are well consistent with the droplet
theory for short-range spin glasses.Comment: 4 pages, 5 figures; The text is slightly changed, the figures 3, 4
and 5 are changed, and a few references are adde
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
Real space analysis of inherent structures
We study a generalization of the one-dimensional disordered Potts model,
which exhibits glassy properties at low temperature. The real space properties
of inherent structures visited dynamically are analyzed through a decomposition
into domains over which the energy is minimized. The size of these domains is
distributed exponentially, defining a characteristic length scale which grows
in equilibrium when lowering temperature, as well as in the aging regime at a
given temperature. In the low temperature limit, this length can be interpreted
as the distance between `excited' domains within the inherent structures.Comment: 7 pages, 8 figures, final versio
Reply to "Comment on Evidence for the droplet picture of spin glasses"
Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation
(MKA), Marinari et al. study in their comment on our paper the link overlap
between two replicas of a three-dimensional Ising spin glass in the presence of
a coupling between the replicas. They claim that the results of the MCS
indicate replica symmetry breaking (RSB), while those of the MKA are trivial,
and that moderate size lattices display the true low temperature behavior. Here
we show that these claims are incorrect, and that the results of MCS and MKA
both can be explained within the droplet picture.Comment: 1 page, 1 figur
Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. I
We study the dynamics of ordering of a nonconserved Heisenberg magnet. The
dynamics consists of two parts --- an irreversible dissipation into a heat bath
and a reversible precession induced by a torque due to the local molecular
field. For quenches to zero temperature, we provide convincing arguments, both
numerically (Langevin simulation) and analytically (approximate closure scheme
due to Mazenko), that the torque is irrelevant at late times. We subject the
Mazenko closure scheme to systematic numerical tests. Such an analysis, carried
out for the first time on a vector order parameter, shows that the closure
scheme performs respectably well. For quenches to , we show, to , that the torque is irrelevant at the Wilson-Fisher fixed
point.Comment: 13 pages, REVTEX, and 19 .eps figures, compressed, Submitted to Phys.
Rev.
Coarsening Dynamics of a Nonconserved Field Advected by a Uniform Shear Flow
We consider the ordering kinetics of a nonconserved scalar field advected by
a uniform shear flow. Using the Ohta-Jasnow-Kawasaki approximation, modified to
allow for shear-induced anisotropy, we calculate the asymptotic time dependence
of the characteristic length scales, L_parallel and L_perp, that describe the
growth of order parallel and perpendicular to the mean domain orientation. In
space dimension d=3 we find, up to constants, L_parallel = gamma t^{3/2},
L_perp = t^{1/2}, where gamma is the shear rate, while for d = 2 we find
L_parallel = gamma^{1/2} t (ln t)^{1/4}, L_perp = gamma^{-1/2}(ln t)^{-1/4} .
Our predictions for d=2 can be tested by experiments on twisted nematic liquid
crystals.Comment: RevTex, 4 page
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