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1.
A complex symplectic structure on a Lie algebra h is an integrable complex structure J with a closed non-degenerate (2,0)-form. It is determined by J and the real part Ω of the (2,0)-form. Suppose that h is a semi-direct product g?V, and both g and V are Lagrangian with respect to Ω and totally real with respect to J. This note shows that g?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω and J are isomorphic. 相似文献
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Let M be a symplectic symmetric space, and let ?:M→V be an extrinsic symplectic symmetric immersion in the sense of Krantz and Schwachhöfer (2010) [7], i.e., (V,Ω) is a symplectic vector space and ? is an injective symplectic immersion such that for each point p∈M, the geodesic symmetry in p is compatible with the reflection in the affine normal space at ?(p). 相似文献
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Denise A. do Nascimento Minos A. Neto J. Ricardo de Sousa Josefa T. Pacobahyba 《Journal of magnetism and magnetic materials》2012
In this paper we study the critical behavior of a two-sublattice Ising model on an anisotropic square lattice in both uniform longitudinal (H ) and transverse (Ω) fields by using the effective-field theory. The model consists of ferromagnetic interaction Jx in the x direction and antiferromagnetic interaction Jy in the y direction in the presence of the H and Ω fields. We obtain the phase diagrams in the H–T and Ω–T planes changing values of the Ω and H parameters, respectively for fixed value at λ=Jx/Jy=1. At null temperature, the ground state phase diagram in the Ω–H plane for several values of λ parameter is analyzed. In the particular case of λ=1 we compare our results with mean-field theory (MFT) and was not observed reentrant behavior around of the critical field Hc/Jy=2.0 for Ω=0 by using EFT. 相似文献
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Magnetic properties of the bond and crystal field dilution spin-3/2 Blume–Capel model in an external magnetic field (h) on simple cubic lattice are studied by using the effective field theory. In the m−T plane, the degeneracy of the magnetization (m) is affected by the concentration of bond or crystal field dilution at low temperature (T). The magnetization curves can appear to fluctuate in certain regions of negative crystal field. In the m−h plane, the initial magnetization curve has an irregular behavior due to the introduction of bond dilution. The crystal field dilution has the influence on the process of magnetic domain displacement. In the χ−h plane, there exists one susceptibility (χ) shoulder and one step for different negative crystal field. The susceptibility curve takes on the feature of multi-peaks distribution under bond and crystal field dilution conditions. 相似文献
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The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused R-matrices and K-matrices, we obtain certain closed operator identities and conditions, which allow us to construct an inhomogeneous T−Q relation and the associated Bethe Ansatz equations accounting for the eigenvalues of the transfer matrix. 相似文献
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We discuss space-time symmetric Hamiltonian operators of the form H=H0+igH′, where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<gc, where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g>0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries. 相似文献
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The random-crystal field spin-1 Blume–Capel model is investigated by the lowest approximation of the cluster-variation method which is identical to the mean-field approximation. The crystal field is either turned on randomly with probability p or turned off with q=1−p in a bimodal distribution. Then the phase diagrams are constructed on the crystal field (Δ)–temperature (kT/J) planes for given values of p and on the (kT/J,p) planes for given Δ by studying the thermal variations of the order parameters. In the latter, we only present the second-order phase transition lines, because of the existence of irregular wiggly phase transitions which are not good enough to construct lines. In addition to these phase transitions, the model also yields tricritical points for all values of p and the reentrant behavior at lower p values. 相似文献
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Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ? and −?−1 are constructed using the technique of intertwining vectors for elliptic L-operator. They are expressed in terms of elliptic hypergeometric series with operator argument. The intertwining operators obtained (W-operators) serve as building blocks for the elliptic R-matrix which intertwines tensor product of two L-operators taken in infinite-dimensional representations of the Sklyanin algebra with arbitrary spin. The Yang–Baxter equation for this R-matrix follows from simpler equations of the star–triangle type for the W-operators. A natural graphic representation of the objects and equations involved in the construction is used. 相似文献
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A cosmological model has been constructed with Gauss–Bonnet-scalar interaction, where the Universe starts with exponential expansion but encounters infinite deceleration, q→∞ and infinite equation of state parameter, w→∞. During evolution it subsequently passes through the stiff fluid era, q=2, w=1, the radiation dominated era, q=1, w=1/3 and the matter dominated era, q=1/2, w=0. Finally, deceleration halts, q=0, w=−1/3, and it then encounters a transition to the accelerating phase. Asymptotically the Universe reaches yet another inflationary phase q→−1, w→−1. Such evolution is independent of the form of the potential and the sign of the kinetic energy term, i.e., even a non-canonical kinetic energy is unable to phantomize (w<−1) the model. 相似文献
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The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T), frequency (w), Onsager coefficient (γ) and external magnetic field (H) near the second-order (Tc) and first-order (Tt) phase transition temperatures are examined for given coordination numbers q on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α). Our investigations revealed that only one peak is obtained near Tt and three peaks are found near Tc when the Onsager coefficient is varied at a given constant frequency for q=3. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4 and 6 near Tc. The sound attenuation peaks are observed near Tt at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear. 相似文献
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We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H and transverse magnetic field Ω. Using the effective-field theory (EFT) with correlation in cluster with N=1 spin we calculate the thermodynamic properties as a function of temperature with values H and Ω fixed. The model consists of ferromagnetic interaction Jx in the x direction and antiferromagnetic interaction Jy in the y direction, and it is found that for H/Jy∈[0,2] the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=Jx/Jy=1 (isotropic square lattice). 相似文献
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A new Poisson structure is defined on a subspace of the Kupershmidt algebra, isomorphic to the space H of n×n Hermitian matrices. The new Poisson structure is of Lie–Poisson type with respect to the standard Lie bracket of H. This Poisson structure (together with two already known ones, obtained through a r-matrix technique) allows to construct an extension of the periodic Toda lattice with n particles that fits in a trihamiltonian recurrence scheme. Some explicit examples of the construction and of the first integrals found in this way are given. 相似文献
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Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0 transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0 1D insulator the charge stiffness D(T) vanishes for T>0 and finite values of the on-site repulsion U in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T and U>0 it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0 and vanishes for U>0 is found to result from a general transition from a conductor to an insulator or resistor occurring at U=Uc=0 for all finite temperatures T>0. (At T=0 such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the η-spin SU(2) symmetry with the hidden U(1) symmetry beyond SO(4) is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model. 相似文献
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J. Lehmann-Lejeune in [J. Lehmann-Lejeune, Cohomologies sur le fibré transverse à un feuilletage, C.R.A.S. Paris 295 (1982), 495–498] defined on the transverse bundle V to a foliation on a manifold M, a zero-deformable structure J such that J2=0 and for every pair of vector fieldsX,Y on M: [JX,JY]−J[JX,Y]−J[X,JY]+J2[X,Y]=0. For every open set Ω of V, J. Lehmann-Lejeune studied the Lie Algebra LJ(Ω) of vector fields X defined on Ω such that the Lie derivative L(X)J is equal to zero i.e., for each vector field Yon Ω: [X,JY]=J[X,Y] and showed that for every vector field X on Ω such thatX∈KerJ, we can write X=∑[Y,Z] where ∑is a finite sum and Y,Z belongs to LJ(Ω)∩(KerJ|Ω). 相似文献
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