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The evolution of rhythmic cognition: New perspectives and technologies in comparative research
Music is a pervasive phenomenon in human culture, and musical rhythm is virtually present in all musical traditions. Research on the evolution and cognitive underpinnings of rhythm can benefit from a number of approaches. We outline key concepts and definitions, allowing fine-grained analysis of rhythmic cognition in experimental studies. We advocate comparative animal research as a useful approach to answer questions about human music cognition and review experimental evidence from different species. Finally, we suggest future directions for research on the cognitive basis of rhythm. Apart from research in semi-natural setups, possibly allowed by “drum set for chimpanzees” prototypes presented here for the first time, mathematical modeling and systematic use of circular statistics may allow promising advances
Magnetic and Thermodynamic Properties of the Collective Paramagnet-Spin Liquid Pyrochlore Tb2Ti2O7
In a recent letter [Phys. Rev. Lett. {\bf 82}, 1012 (1999)] it was found that
the Tb magnetic moments in the TbTiO pyrochlore lattice of
corner-sharing tetrahedra remain in a {\it collective paramagnetic} state down
to 70mK. In this paper we present results from d.c. magnetic susceptibility,
specific heat data, inelastic neutron scattering measurements, and crystal
field calculations that strongly suggest that (1) the Tb ions in
TbTiO possess a moment of approximatively 5, and (2)
the ground state tensor is extremely anisotropic below a temperature of
K, with Ising-like Tb magnetic moments confined to point along
a local cubic direction
dramatically reduces the frustration otherwise present in a Heisenberg
pyrochlore antiferromagnet. The results presented herein underpin the
conceptual difficulty in understanding the microscopic mechanism(s) responsible
for TbTiO failing to develop long-range order at a temperature of
the order of the paramagnetic Curie-Weiss temperature K. We suggest that dipolar interactions and extra perturbative exchange
coupling(s)beyond nearest-neighbors may be responsible for the lack of ordering
of TbTiO.Comment: 8 POSTSCRIPT figures included. Submitted to Physical Review B.
Contact: [email protected]
Ferroelectric and Dipolar Glass Phases of Non-Crystalline Systems
In a recent letter [Phys. Rev. Lett. {\bf 75}, 2360 (1996)] we briefly
discussed the existence and nature of ferroelectric order in positionally
disordered dipolar materials. Here we report further results and give a
complete description of our work. Simulations of randomly frozen and
dynamically disordered dipolar soft spheres are used to study ferroelectric
ordering in non-crystalline systems. We also give a physical interpretation of
the simulation results in terms of short- and long-range interactions. Cases
where the dipole moment has 1, 2, and 3 components (Ising, XY and XYZ models,
respectively) are considered. It is found that the Ising model displays
ferroelectric phases in frozen amorphous systems, while the XY and XYZ models
form dipolar glass phases at low temperatures. In the dynamically disordered
model the equations of motion are decoupled such that particle translation is
completely independent of the dipolar forces. These systems spontaneously
develop long-range ferroelectric order at nonzero temperature despite the
absence of any fined-tuned short-range spatial correlations favoring dipolar
order. Furthermore, since this is a nonequilibrium model we find that the
paraelectric to ferroelectric transition depends on the particle mass. For the
XY and XYZ models, the critical temperatures extrapolate to zero as the mass of
the particle becomes infinite, whereas, for the Ising model the critical
temperature is almost independent of mass and coincides with the ferroelectric
transition found for the randomly frozen system at the same density. Thus in
the infinite mass limit the results of the frozen amorphous systems are
recovered.Comment: 25 pages (LATEX, no macros). 11 POSTSCRIPT figures enclosed.
Submitted to Phisical Review E. Contact: [email protected]
Non-trivial fixed point structure of the two-dimensional +-J 3-state Potts ferromagnet/spin glass
The fixed point structure of the 2D 3-state random-bond Potts model with a
bimodal (J) distribution of couplings is for the first time fully
determined using numerical renormalization group techniques. Apart from the
pure and T=0 critical fixed points, two other non-trivial fixed points are
found. One is the critical fixed point for the random-bond, but unfrustrated,
ferromagnet. The other is a bicritical fixed point analogous to the bicritical
Nishimori fixed point found in the random-bond frustrated Ising model.
Estimates of the associated critical exponents are given for the various fixed
points of the random-bond Potts model.Comment: 4 pages, 2 eps figures, RevTex 3.0 format requires float and epsfig
macro
Stability of the Bragg glass phase in a layered geometry
We study the stability of the dislocation-free Bragg glass phase in a layered
geometry consisting of coupled parallel planes of d=1+1 vortex lines lying
within each plane, in the presence of impurity disorder. Using renormalization
group, replica variational calculations and physical arguments we show that at
temperatures the 3D Bragg glass phase is always stable for weak
disorder. It undergoes a weakly first order transition into a decoupled 2D
vortex glass upon increase of disorder.Comment: RevTeX. Submitted to EP
Proposal for a [111] Magnetization Plateau in the Spin Liquid State of Tb2Ti2O7
Despite a Curie-Weiss temperature K, the Tb2Ti2O7
pyrochlore magnetic material lacks long range magnetic order down to at least
mK. It has recently been proposed that the low temperature
collective paramagnetic or spin liquid regime of this material may be akin to a
spin ice state subject to both thermal and quantum fluctuations a {\it
quantum spin ice} (QSI) of sorts. Here we explore the effect of a magnetic
field along the direction on the QSI state. To do so, we
investigate the magnetic properties of a microscopic model of Tb2Ti2O7 in an
independent tetrahedron approximation in a finite along . Such
a model describes semi-quantitatively the collective paramagnetic regime where
nontrivial spin correlations start to develop at the shortest lengthscale, that
is over a single tetrahedron, but where no long range order is yet present. Our
results show that a magnetization plateau develops at low temperatures as the
system develops ferromagnetic spin-ice-like "two-in/two-out"
correlations at the shortest lengthscale. From these results, we are led to
propose that the observation of such a [111] magnetization plateau in Tb2Ti2O7
would provide compelling evidence for a QSI at in this material and
help guide the development of a theory for the origin of its spin liquid state.Comment: 6 pages, 3 figure
Neutron spectroscopic study of crystal field excitations in Tb2Ti2O7 and Tb2Sn2O7
We present time-of-flight inelastic neutron scattering measurements at low
temperature on powder samples of the magnetic pyrochlore oxides Tb2Ti2O7 and
Tb2Sn2O7. These two materials possess related, but different ground states,
with Tb2Sn2O7 displaying "soft" spin ice order below Tn~0.87 K, while Tb2Ti2O7
enters a hybrid, glassy spin ice state below Tg~0.2 K. Our neutron
measurements, performed at T=1.5 K and 30 K, probe the crystal field states
associated with the J=6 states of Tb3+ within the appropriate Fd\bar{3}m
pyrochlore environment. These crystal field states determine the size and
anisotropy of the Tb3+ magnetic moment in each material's ground state,
information that is an essential starting point for any description of the
low-temperature phase behavior and spin dynamics in Tb2Ti2O7 and Tb2Sn2O7.
While these two materials have much in common, the cubic stanate lattice is
expanded compared to the cubic titanate lattice. As our measurements show, this
translates into a factor of ~2 increase in the crystal field bandwidth of the
2J+1=13 states in Tb2Ti2O7 compared with Tb2Sn2O7. Our results are consistent
with previous measurements on crystal field states in Tb2Sn2O7, wherein the
ground state doublet corresponds primarily to m_J=|\pm 5> and the first excited
state doublet to mJ=|\pm 4>. In contrast, our results on Tb2Ti2O7 differ
markedly from earlier studies, showing that the ground state doublet
corresponds to a significant mixture of mJ=|\pm 5>, |\mp 4>, and |\pm 2>, while
the first excited state doublet corresponds to a mixture of mJ=|\pm 4>, |\mp
5>, and |\pm 1>. We discuss these results in the context of proposed mechanisms
for the failure of Tb2Ti2O7 to develop conventional long-range order down to 50
mK.Comment: 12 pages, 6 figures. Version is the same as the published one, except
for figure placement on page
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