The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.     

PT Symmetry in Quantum Field Theory

The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian. The Hermiticity of H guarantees that the energy spectrum is real and that the time evolution is unitary (probability preserving). In this talk we investigate an alternative formulation of quantum mechanics in which the mathematical requirement of Hermiticity is replaced by the more physically transparent condition of space-time reflection (PT) symmetry. We show that if the PT symmetry of a Hamiltonian H is not broken, then the spectrum of H is real. Examples of PT-symmetric non-Hermitian Hamiltonians are H=p ²+ix ³ and H=p ²-x ⁴. The crucial question is whether PT-symmetric Hamiltonians specify physically acceptable quantum theories in which the norms of states are positive and the time evolution is unitary. The answer is that a Hamiltonian that has an unbroken PT symmetry also possesses a physical symmetry that we call C. Using C, we show how to construct an inner product whose associated norm is positive definite. The result is a new class of fully consistent complex quantum theories. Observables exhibit CPT symmetry, probabilities are positive, and the dynamics is governed by unitary time evolution.     

Corner spontaneous magnetization

Details are given of a new method allowing an exact calculation of the spontaneous magnetization in the corner as well as along the edge at an arbitrary distance of the corner for a rectangular planar Ising ferromagnet.     

Magnetic properties of lanthanum orthoferrite fine powders prepared by different chemical routes

Fine powders of lanthanum iron oxide, LaFeO₃, have been prepared by solid state reaction as well as sol-gel synthesis and nebulized spray pyrolysis. Structures, morphologies and magnetic susceptibility measurements of these powders have been examined. The powders prepared by all the three low-temperature routes contain nearly spherical particles with an average diameter of 40 nm. These samples show a lower Neel temperature than the powder prepared by solid state reaction besides showing much lower magnetic susceptibility at low temperatures. Dedicated to Professor C N R Rao on his 70th birthday     

Monte Carlo simulations on magnetic behavior of a spin-chain system in triangular lattice doped with antiferromagnetic bonds

A three-dimensional Ising-like model doped with anti-ferromagnetic (AFM) bonds is proposed to investigate the magnetic properties of a doped triangular spin-chain system by using a Monte-Carlo simulation. The simulated results indicate that a steplike magnetization behavior is very sensitive to the concentration of AFM bonds. A low concentration of AFM bonds can suppress the stepwise behavior considerably, in accordance with doping experiments on Ca₃Co₂O₆. The analysis of spin snapshots demonstrates that the AFM bond doping not only breaks the ferromagnetic ordered linear spin chains along the hexagonal c-axis but also has a great influence upon the spin configuration in the ab-plane.      

On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).     

Phase uniqueness and correlation length in diluted-field Ising models

The diluted-field Ising model, a random nonnegative field ferromagnetic model, is shown to have a unique Gibbs measure with probability I when the field mean is positive. Our methods involve comparisons with ordinary uniform field Ising models. They yield as a corollary a way of obtaining spontaneous magnetization through the application of a vanishing random magnetic field. The correlation lengths of this model defined as (lim _n-(1/n) log ₀; _n)^-1, wheren is the site on the first coordinate axis at distancen from the origin and ₀; _n is the origin ton two-point truncated correlation function, is non-random. We derive an upper bound for it in terms of the correlation length of an ordinary nonrandom model with uniform field related to the field distribution of the diluted model.     

The Influence of Yb Doping and Sintering Conditions on the Magnetocaloric and Mechanical Properties of EuS

For this work, europium monosulfide (EuS) powders were prepared by sulfurizing Eu₂O₃ powder with CS₂ gas. The synthesized EuS powders were sintered by SPS at temperatures in the 800–1600 °C range for 0.33–1 h at 50 MPa under vacuum conditions. The influences of Yb doping and sintering conditions on the magnetocaloric and mechanical properties of EuS were investigated systematically. An increase in sintering temperature caused the rise of lattice parameters of EuS, whereas Yb doping caused them to drop. SEM showed that the grain size of the EuS increased with sintering temperatures in the 1000–1400 °C range. Higher sintering temperatures can enlarge the magnetizability and saturation magnetization of EuS compact. On the contrary, Yb doping can weaken the magnetizability and saturation magnetization of EuS compact. All sintered polycrystalline EuS compacts had weaker thermomagnetic irreversibility and lower magnetic anisotropy.     

MAGNETOMECHANICAL BEHAVIORS OF GIANT MAGNETOSTRICTIVE MATERIALS

The Laves phase alloy Tb-Dy-Fe, commercially known as Terfenol-D, exhibits the giant room-temperature magnetostriction at moderate field strength of a few kOe due to its combination of high magnetostriction and low magnetocrystalline anisotropic energy. Thus, this pseudobinary rare earth iron compound has found quite a number of applications such as in magnetomechanical transducers, actuators and adaptive vibration control systems. The simultaneous measurements of magnetostriction and magnetization at various fixed compressive pre-stresses applied in the axial direction for Tb0.3Dy0.7Fe1.95 samples are presented. The results show that the magnetostriction increases with increasing compressive stress until it reaches 1742 ×10^6 under 25 MPa, so does the coercive magnetic field. And the hysteresis loop area for magnetization and magnetostriction also increases with the increment of applied compressive stresses. But the maximum magnetic susceptibility χ（dM/dH） is obtained under zero stress field and the strain derivative dλ/dH increases to the highest amplitude of 0.039×10^-6 A^-1m at a stress level of 5 MPa. In the strain versus magnetization intensity curve, the initial fiat stage mainly consisting of a 180° domain wall motion becomes shorter with increasing stress. It means more initial domains are driven to the transversal direction under the compressive stress before magnetization, which is consistent with the improvement of the magnetostriction.     

Migration behavior and enantioseparation of hydrobenzoin and structurally related compounds in capillary zone electrophoresis with a dual cyclodextrin system consisting of heptakis-(2,3-dihydroxy-6-O-sulfo)-beta-cyclodextrin and beta-cyclodextrin

Migration behavior and enantioseparation of racemic hydrobenzoin and structurally related compounds, including benzoin and benzoin methyl ether, in CZE with a dual CD system consisting of heptakis-(2,3-dihydroxy-6-O-sulfo)-beta-CD (SI-S-beta-CD) and beta-CD as chiral selectors in the presence and absence of borate complexation at pH 9.0 were investigated. The results indicate that enantioseparation of hydrobenzoin is mainly governed by CD complexation of hydrobenzoin-borate complexes with SI-S-beta-CD when SI-S-beta-CD concentration is relatively high. Whereas CD complexation of hydrobenzoin-borate complexes with beta-CD plays a significant role in enantioseparation when SI-S-beta-CD concentration is comparatively low. The (S,S)-enantiomer of the hydrobenzoin-borate complex was found to interact more strongly than the corresponding (R,R)-enantiomer with both SI-S-beta-CD and beta-CD. These two types of CD show the same chiral recognition pattern, but they exhibit opposite effects on the mobility of the enantiomers of hydrobenzoin-borate complexes. Enantiomer migration reversal of hydrobenzoin occurred in the presence of borate complexation when varying the concentration of beta-CD, while keeping SI-S-beta-CD at a relatively low concentration. Binding constants of the enantiomers of benzoin-related compounds to beta-CD and those of hydrobenzoin-borate complexes to SI-beta-CD were evaluated; the mobility contributions of all complex species to the effective mobility of the enantiomers of hydrobenzoin as a function of beta-CD concentration in a borate buffer were analyzed. In addition, comparative studies on the enantioseparation of benzoin-related compounds with SI-S-beta-CD and with randomly sulfate-substituted beta-CD were made.