90,394 research outputs found

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

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    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

    Carrier States and Ferromagnetism in Diluted Magnetic Semiconductors

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    Applying the dynamical coherent potential approximation to a simple model, we have systematically studied the carrier states in A1−xA_{1-x}MnxB_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 Ga1−x_{1-x}Mnx_xAs. 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

    Thermodynamical Bethe Ansatz and Condensed Matter

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    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

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

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    A nonlinear susceptibilities (the third derivative of a magnetization mSm_S by a magnetic field hh ) of the SS=1/2 ferromagnetic Heisenberg chain and the classical Heisenberg chain are calculated at low temperatures T.T. In both chains the nonlinear susceptibilities diverge as T−6T^{-6} and a linear susceptibilities diverge as T−2.T^{-2}. The arbitrary spin SS Heisenberg ferromagnet [[ H=∑i=1N{−JSiSi+1−(h/S)Siz}{\cal H} = \sum_{i=1}^{N} \{ - J{\bf S}_{i} {\bf S}_{i+1} - (h/S) S_{i}^{z} \} (J>0),(J>0), ]] has a scaling relation between mS,m_S, hh and T:T: mS(T,h)=F(S2Jh/T2).m_S(T,h) = F( S^2 Jh/T^2). The scaling function F(x)F(x)=(2xx/3)-(44x3x^{3}/135) + O(x5x^{5}) is common to all values of spin S.S.Comment: 16 pages (revtex 2.0) + 6 PS figures upon reques

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

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    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

    Magnetic Resonant X-Ray Scattering in KCuF3

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    We study the magnetic resonant x-ray scattering (RXS) spectra around the KK edge of Cu in KCuF3_3 on the basis of an {\em ab initio} calculation. We use the full-potential linearlized augmented plane wave method in the LDA+U+U scheme, and introduce the lattice distortion as inputs of the calculation. We obtain finite intensity on magnetic superlattice spots, about three orders of magnitude smaller than on orbital superlattice spots, by taking account of the spin-orbit interaction (SOI). No intensity appears without the SOI, indicating that the intensity arises not from the spin polarization but from the orbital polarization in 4p4p states. The present calculation reproduces well the experimental spectra as functions of photon energy and of azimuthal angle. We also calculate the RXS intensity on orbital superlattice spots. It is found that the intensity increases with increasing Jahn-Teller distortion. The spectra remain nearly the same in the nonmagnetic state given by the simple LDA, in which the orbital polarization in the 3d states is much smaller. This strongly suggests that the intensity on orbital spots is mainly controlled by the lattice distortion, not by the 3d orbital order itself.Comment: 7 pages, 8 figures, Submitted to PRB, RevTeX

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

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

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

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    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

    Universal low-temperature properties of quantum and classical ferromagnetic chains

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    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
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