74,023 research outputs found

### Takahashi Integral Equation and High-Temperature Expansion of the Heisenberg Chain

Recently a new integral equation describing the thermodynamics of the 1D
Heisenberg model was discovered by Takahashi. Using the integral equation we
have succeeded in obtaining the high temperature expansion of the specific heat
and the magnetic susceptibility up to O((J/T)^{100}). This is much higher than
those obtained so far by the standard methods such as the linked-cluster
algorithm. Our results will be useful to examine various approximation methods
to extrapolate the high temperature expansion to the low temperature region.Comment: 5 pages, 4 figures, 2 table

### Thermodynamical Bethe Ansatz and Condensed Matter

The basics of the thermodynamic Bethe ansatz equation are given. The simplest
case is repulsive delta function bosons, the thermodynamic equation contains
only one unknown function. We also treat the XXX model with spin 1/2 and the
XXZ model and the XYZ model. This method is very useful for the investigation
of the low temperature thermodynamics of solvable systems.Comment: 52 pages, 6 figures, latex, lamuphys.st

### Carrier States and Ferromagnetism in Diluted Magnetic Semiconductors

Applying the dynamical coherent potential approximation to a simple model, we
have systematically studied the carrier states in $A_{1-x}$Mn$_xB$-type diluted
magnetic semiconductors (DMS's). The model calculation was performed for three
typical cases of DMS's: The cases with strong and moderate exchange
interactions in the absence of nonmagnetic potentials, and the case with strong
attractive nonmagnetic potentials in addition to moderate exchange interaction.
When the exchange interaction is sufficiently strong, magnetic impurity bands
split from the host band. Carriers in the magnetic impurity band mainly stay at
magnetic sites, and coupling between the carrier spin and the localized spin is
very strong. The hopping of the carriers among the magnetic sites causes
ferromagnetism through a {\it double-exchange (DE)-like} mechanism. We have
investigated the condition for the DE-like mechanism to operate in DMS's. The
result reveals that the nonmagnetic attractive potential at the magnetic site
assists the formation of the magnetic impurity band and makes the DE-like
mechanism operative by substantially enhancing the effect of the exchange
interaction. Using conventional parameters we have studied the carrier states
in Ga$_{1-x}$Mn$_x$As. The result shows that the ferromagnetism is caused
through the DE-like mechanism by the carriers in the bandtail originating from
the impurity states.Comment: 20 pages, 14 figure

### The Free Energy and the Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

A nonlinear susceptibilities (the third derivative of a magnetization $m_S$
by a magnetic field $h$ ) of the $S$=1/2 ferromagnetic Heisenberg chain and the
classical Heisenberg chain are calculated at low temperatures $T.$ In both
chains the nonlinear susceptibilities diverge as $T^{-6}$ and a linear
susceptibilities diverge as $T^{-2}.$ The arbitrary spin $S$ Heisenberg
ferromagnet $[$ ${\cal H} = \sum_{i=1}^{N} \{ - J{\bf S}_{i} {\bf S}_{i+1} -
(h/S) S_{i}^{z} \}$ $(J>0),$ $]$ has a scaling relation between $m_S,$ $h$ and
$T:$ $m_S(T,h) = F( S^2 Jh/T^2).$ The scaling function
$F(x)$=(2$x$/3)-(44$x^{3}$/135) + O($x^{5}$) is common to all values of spin
$S.$Comment: 16 pages (revtex 2.0) + 6 PS figures upon reques

### Integrable Magnetic Model of Two Chains Coupled by Four-Body Interactions

An exact solution for an XXZ chain with four-body interactions is obtained
and its phase diagram is determined. The model can be reduced to two chains
coupled by four-body interactions, and it is shown that the ground state of the
two-chain model is magnetized in part. Furthermore, a twisted four-body
correlation function of the anti-ferromagnetic Heisenberg chain is obtained.Comment: 7 pages, LaTeX, to be published in J. Phys. Soc. Jpn., rederived the
mode

### On the location of two blow up points on an annulus for the mean field equation

We consider the mean field equation on two-dimensional annular domains, and
prove that if $P$ and $Q$ are two blow up points of a blowing-up solution
sequence of the equation, then we must have $P=-Q$.Comment: To appear in CRA

### Universal low-temperature properties of quantum and classical ferromagnetic chains

We identify the critical theory controlling the universal, low temperature,
macroscopic properties of both quantum and classical ferromagnetic chains. The
theory is the quantum mechanics of a single rotor. The mapping leads to an
efficient method for computing scaling functions to high accuracy.Comment: 4 pages, 2 tables and 3 Postscript figure

### Modified Spin Wave Analysis of Low Temperature Properties of Spin-1/2 Frustrated Ferromagnetic Ladder

Low temperature properties of the spin-1/2 frustrated ladder with
ferromagnetic rungs and legs, and two different antiferromagnetic next nearest
neighbor interaction are investigated using the modified spin wave
approximation in the region with ferromagnetic ground state. The temperature
dependence of the magnetic susceptibility and magnetic structure factors is
calculated. The results are consistent with the numerical exact diagonalization
results in the intermediate temperature range. Below this temperature range,
the finite size effect is significant in the numerical diagonalization results,
while the modified spin wave approximation gives more reliable results. The low
temperature properties near the limit of the stability of the ferromagnetic
ground state are also discussed.Comment: 9 pages, 8 figure

### Nuclear Astrophysics

Nuclear astrophysics is that branch of astrophysics which helps understanding
some of the many facets of the Universe through the knowledge of the microcosm
of the atomic nucleus. In the last decades much advance has been made in
nuclear astrophysics thanks to the sometimes spectacular progress in the
modelling of the structure and evolution of the stars, in the quality and
diversity of the astronomical observations, as well as in the experimental and
theoretical understanding of the atomic nucleus and of its spontaneous or
induced transformations. Developments in other sub-fields of physics and
chemistry have also contributed to that advance. Many long-standing problems
remain to be solved, however, and the theoretical understanding of a large
variety of observational facts needs to be put on safer grounds. In addition,
new questions are continuously emerging, and new facts endanger old ideas. This
review shows that astrophysics has been, and still is, highly demanding to
nuclear physics in both its experimental and theoretical components. On top of
the fact that large varieties of nuclei have to be dealt with, these nuclei are
immersed in highly unusual environments which may have a significant impact on
their static properties, the diversity of their transmutation modes, and on the
probabilities of these modes. In order to have a chance of solving some of the
problems nuclear astrophysics is facing, the astrophysicists and nuclear
physicists are obviously bound to put their competence in common, and have
sometimes to benefit from the help of other fields of physics, like particle
physics, plasma physics or solid-state physics.Comment: LaTeX2e with iopart.cls, 84 pages, 19 figures (graphicx package), 374
updated references. Published in Reports on Progress in Physics, vol.62, pp.
395-464 (1999

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