1,248 research outputs found
Inertial modes in slowly rotating stars : an evolutionary description
We present a new hydro code based on spectral methods using spherical
coordinates. The first version of this code aims at studying time evolution of
inertial modes in slowly rotating neutron stars. In this article, we introduce
the anelastic approximation, developed in atmospheric physics, using the mass
conservation equation to discard acoustic waves. We describe our algorithms and
some tests of the linear version of the code, and also some preliminary linear
results. We show, in the Newtonian framework with differentially rotating
background, as in the relativistic case with the strong Cowling approximation,
that the main part of the velocity quickly concentrates near the equator of the
star. Thus, our time evolution approach gives results analogous to those
obtained by Karino {\it et al.} \cite{karino01} within a calculation of
eigenvectors. Furthermore, in agreement with the work of Lockitch {\it et al.}
\cite{lockandf01}, we found that the velocity seems to always get a
non-vanishing polar part.Comment: 36 pages, 27 figures, accepted for publication in Phys. Rev. D
(discussion added in the introduction
Study of Chirality in the Two-Dimensional XY Spin Glass
We study the chirality in the Villain form of the XY spin glass in
two--dimensions by Monte Carlo simulations. We calculate the chiral-glass
correlation length exponent and find that
in reasonable agreement with
earlier studies. This indicates that the chiral and phase variables are
decoupled on long length scales and diverge as with {\em different}
exponents, since the spin-glass correlation length exponent was found, in
earlier studies, to be about 1.0.Comment: 4 pages. Latex file and 4 embedded postscript files are included in a
self-unpacking compressed tar file. A postscript version is available at
ftp://chopin.ucsc.edu/pub/xysg.p
Inertial modes in stratified rotating neutron stars : An evolutionary description
With (non-barotropic) equations of state valid even when the neutron, proton
and electron content of neutron star cores is not in beta equilibrium, we study
inertial and composition gravity modes of relativistic rotating neutron stars.
We solve the relativistic Euler equations in the time domain with a three
dimensional numerical code based on spectral methods, in the slow rotation,
relativistic Cowling and anelastic approximations. Principally, after a short
description of the gravity modes due to smooth composition gradients, we focus
our analysis on the question of how the inertial modes are affected by
non-barotropicity of the nuclear matter. In our study, the deviation with
respect to barotropicity results from the frozen composition of non-superfluid
matter composed of neutrons, protons and electrons, when beta equilibrium is
broken by millisecond oscillations. We show that already for moderatly fast
rotating stars the increasing coupling between polar and axial modes makes
those two cases less different than for very slowly rotating stars. In
addition, as we directly solve the Euler equations, without coupling only a few
number of spherical harmonics, we always found, for the models that we use, a
discrete spectrum for the inertial mode. Finally, we find that, for
non-barotropic stars, the frequency of this mode, which is our main focus,
decreases in a non-negligible way, whereas the time dependence of the energy
transfer between polar and axial modes is substantially different due to the
existence of low-frequencies gravity modes.Comment: 34 pages, 24 figures, published versio
MHD of rotating compact stars with spectral methods: description of the algorithm and tests
A flexible spectral code for the study of general relativistic
magnetohydrodynamics is presented. Aiming at investigating the physics of
slowly rotating magnetized compact stars, this new code makes use of various
physically motivated approximations. Among them, the relativistic anelastic
approximation is a key ingredient of the current version of the code. In this
article, we mainly outline the method, putting emphasis on algorithmic
techniques that enable to benefit as much as possible of the non-dissipative
character of spectral methods, showing also a potential astrophysical
application and providing a few illustrative tests.Comment: 15 pages, 4 figures (new figure added, misprints corrected) Article
accepted for publication in a special issue of Classical and Quantum Gravity
"New Frontiers in Numerical Relativity
Dipolar spin correlations in classical pyrochlore magnets
We study spin correlations for the highly frustrated classical pyrochlore
lattice antiferromagnets with O(N) symmetry in the limit T->0. We conjecture
that a local constraint obeyed by the extensively degenerate ground states
dictates a dipolar form for the asymptotic spin correlations, at all N 2
for which the system is paramagnetic down to T=0. We verify this conjecture in
the cases N=1 and N=3 by simulations and to all orders in the 1/N expansion
about the solvable N=infinity limit. Remarkably, the N=infinity formulae are an
excellent fit, at all distances, to the correlators at N=3 and even at N=1.
Thus we obtain a simple analytical expression also for the correlations of the
equivalent models of spin ice and cubic water ice, I_h.Comment: 4 pages revtex
Effect of weak disorder in the Fully Frustrated XY model
The critical behaviour of the Fully Frustrated XY model in presence of weak
positional disorder is studied in a square lattice by Monte Carlo methods. The
critical exponent associated to the divergence of the chiral correlation length
is found to be equal to 1.7 already at very small values of disorder.
Furthermore the helicity modulus jump is found larger than the universal value
expected in the XY model.Comment: 8 pages, 4 figures (revtex
Kink-Antikink Unbinding Transition in the Two Dimensional Fully Frustrated XY Model
We carry out the first numerical simulations to directly confirm the
existence of a kink-antikink unbinding transition, T_w, along Ising-like domain
walls in the two dimensional fully frustrated XY model. We comment on the
possible implications of kink-antikink unbinding for the bulk phase transitions
of the model.Comment: 8 pages, 10 figures - expanded version of original submission as
accepted by Phys. Rev. B. Some correction to the analysis lead to an increase
in the value of the kink unbinding transition temperatur
Emergent gauge dynamics of highly frustrated magnets
Condensed matter exhibits a wide variety of exotic emergent phenomena such as
the fractional quantum Hall effect and the low temperature cooperative behavior
of highly frustrated magnets. I consider the classical Hamiltonian dynamics of
spins of the latter phenomena using a method introduced by Dirac in the 1950s
by assuming they are constrained to their lowest energy configurations as a
simplifying measure. Focusing on the kagome antiferromagnet as an example, I
find it is a gauge system with topological dynamics and non-locally connected
edge states for certain open boundary conditions similar to doubled
Chern-Simons electrodynamics expected of a spin liquid. These dynamics
are also similar to electrons in the fractional quantum Hall effect. The
classical theory presented here is a first step towards a controlled
semi-classical description of the spin liquid phases of many pyrochlore and
kagome antiferromagnets and towards a description of the low energy classical
dynamics of the corresponding unconstrained Heisenberg models.Comment: Updated with some appendices moved to the main body of the paper and
some additional improvements. 21 pages, 5 figure
Finite-size effects on the Hamiltonian dynamics of the XY-model
The dynamical properties of the finite-size magnetization M in the critical
region T<T_{KTB} of the planar rotor model on a L x L square lattice are
analyzed by means of microcanonical simulations . The behavior of the q=0
structure factor at high frequencies is consistent with field-theoretical
results, but new additional features occur at lower frequencies. The motion of
M determines a region of spectral lines and the presence of a central peak,
which we attribute to phase diffusion. Near T_{KTB} the diffusion constant
scales with system size as D ~ L^{-1.6(3)}.Comment: To be published in Europhysics Letter
Fluctuations and vortex pattern ordering in fully frustrated XY model with honeycomb lattice
The accidental degeneracy of various ground states in a fully frustrated XY
model with a honeycomb lattice is shown to survive even when the free energy of
the harmonic fluctuations is taken into account. The reason for that consists
in the existence of a hidden gauge symmetry between the Hamiltonians describing
the harmonic fluctuations in all these ground states. A particular vortex
pattern is selected only when anharmonic fluctuations are taken into account.
However, the observation of vortex ordering requires relatively large system
size L>>100000.Comment: 4 pages, 2 figures, RevTeX4, a different method is used to find which
state is selected by anharmonic fluctuations, the last third of the text is
completly rewritte
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