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

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

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

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

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

Trans-Magnetosonic Accretion in a Black Hole Magnetosphere

We present the critical conditions for hot trans-fast magnetohydrodynamical (MHD) flows in a stationary and axisymmetric black-hole magnetosphere. To accrete onto the black hole, the MHD flow injected from a plasma source with low velocity must pass through the fast magnetosonic point after passing through the ``inner'' or ``outer'' Alfven point. We find that a trans-fast MHD accretion solution related to the inner Alfven point is invalid when the hydrodynamical effects on the MHD flow dominate at the magnetosonic point, while the other accretion solution related to the outer Alfven point is invalid when the total angular momentum of the MHD flow is seriously large. When both regimes of the accretion solutions are valid in the black hole magnetosphere, we can expect the transition between the two regimes. The variety of these solutions would be important in many highly energetic astrophysical situations.Comment: 27 pages, 12 figures, accepted to Ap

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

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