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