Anisotropic special transition of semi-infinite systems in the 1/n expansion

The effect of the surface magnetic anisotropy on the critical behavior at surfaces is studied by using the 1/n expansion technique. Several surface critical exponents are obtained for the anisotropic special transition at arbitrary spatial dimensions.     

Double-hole binding energy shifts for the 5d transition metals

Recent experimental M₄₅N₆₇N₆₇ Auger energies for Ta, W, Ir, Pt, Au, Hg and Pb are analyzed in terms of the complete screening picture. For the shift in the double-hole (N₆₇N₆₇) binding energy between the free atom and the metal a good agreement is found between theory and experiment. The variation of the shift throughout the 5d series and beyond reflects different types of screening of the two core holes, i.e. a large shift in the case of d-type screening and a considerably smaller shift for sp-type screening.     

Upper bounds on the critical temperature for various ising models

Upper bounds are obtained for spin ±1 systems. In the case of only nearestneighbor interactions on, for example, the square lattice we obtain _cJ>0.3592. The method's strength is seen when considering systems with longer-range interactions. For example, we obtain _cJ>0.360 compared to the previous best bound of _c J 0.345 for the one-dimensional lattice with 1/r ² interactions. The method relies upon an identity between correlation functions and then the use of correlation inequalities to obtain the final bounds.     

New upper bounds for the magnetization in ferromagnetic one-component systems

A collection of upper bounds on the magnetization in ferromagnetic one-component spin systems is derived from generalizations of the mean-field approximation. In particular, it contains sequences of bounds that converge to the true magnetization. The spin systems in question satisfy the GHS-inequality.Institut für Theoretische Physik, Universität Zürich, Zürich, Switzerland     

Anisotropy of positron wave function in 4d transition metals

The positron wave functions have been calculated employing the method of expansion of symmetrized plane waves in some 4d transition metals. Systematics of the positron wave functions along the three symmetry directions [100], [110], [111] in these metals, have been discussed. The anisotropies of the ψ₊ have been found to be strongly dependent upon the crystal symmetries. The results of the band structure calculation of 2γ-angular correlation in Rh and Ag are presented.     

Upper bounds on the critical temperature for the two-dimensional Blume-Emery-Griffiths model

We obtain rigorous upper bounds for the critical temperature associated with second-order phase transitions of the two-dimensional spin-1 BEG model for real values ofK andD coupling constants and forJ0. We use some correlation equalities and inequalities to show the exponential decay of the two-point function characterizing the disordered phase.     

Hyperfine interactions in intermetallic compounds between Gd and 3d transition metals

Measurements of hyperfine interactions at ¹⁵⁵Gd nuclei in metallic compounds between Gd and 3d transition metals and at ⁶¹Ni in GdNi compounds by Mössbauer spectroscopy are reported. The results are discussed in terms of various models proposed for the electronic structure of these compounds. The Gd isomer shifts with respect to metallic Gd are at variance with the model of a strong d electron transfer from rare earths to transition metal ions. From the observation of a linear relation between magnetic hyperfine fields at Gd and at Dy nuclei in corresponding compounds it is inferred that crystal-field induced variations of Dy moments are neglible and that the conduction electron polarization induced by 4f moments is directly related to that caused by 3d moments.     

Analyticity and uniqueness for spin 1/2 classical ferromagnetic lattice systems at low temperatures

Analyticity and uniqueness of correlation functions is investigated for a number of systems by application of Ruelle's theorem on zeros of Asano contracted polynomials to the partition function. To answer the question when the partition function of a system is the Asano contraction of those of subsystems the groups appearing in the low and high temperature expansions are employed.On leave of absence from Department of Physics and Astronomy, Tel Aviv University Ramat-Aviv, Israel.     

Upper bounds on the free energy of random spin systems

The sequence of upper bounds on the quenched free energy of a random spin system considered by Goulart Rosa recently is rederived by an alternative method, and a similar sequence is constructed for the annealed free energy. The dependence of the free energy on interactions between spins is discussed.     

Upper limit on the transition temperature for non-ideal Bose gases

In this paper, we show that for a non-ideal Bose gas there exists an upper limit on the transition temperature above which Bose-Einstein condensation cannot occur regardless of the pressure applied. Such upper limits for some realistic Bose gases are estimated.     

The high temperature expansion of the classical XYZ chain

The β$\beta$-expansion of the Helmholtz free energy (HFE) up to order β¹²${\beta }^{12}$ of the classical XYZ model with a single-ion anisotropy term and external magnetic field is calculated and compared to the numerical solution of Joyce's [Phys. Rev. Lett. 19 (1967) 581] for the XXZ   classical model, with neither single-ion anisotropy term nor external magnetic field. This comparison shows that the derived analytical expansion is valid for intermediate temperatures such as kT/_Jx≈0.5$\mathit{kT}/J_x\approx 0.5$. The specific heat and magnetic susceptibility of the S=2$S=2$ antiferromagnetic chain can be approximated by their respective classical results, within an error of 2.5%$2.5\%$, up to kT/J≈0.8$\mathit{kT}/J\approx 0.8$. For a vanishing external magnetic field the ferromagnetic and antiferromagnetic chains are shown to have the same classical HFE; their behaviour in a non-vanishing external magnetic field is also described.     

Influence of high pressure on the ferromagnetic transition temperature of CrO2

The shift of the Curie temperature of CrO₂ with pressure was determined by ac-susceptibility measurements under hydrostatic pressure up to 5 GPa. These experiments show that ferromagnetism of CrO₂ is suppressed at a rate , which is close to recent theoretical estimates.     

Quantum nonintegrability and the classical limit for usp(4) systems

We investigate the transition from integrability to chaos in a system built of usp(4) elements, both in the quantum case and in its classical limit, obtained using coherent states. This algebraic Hamiltonian consists in an integrable term plus a nonlinear perturbation, and we see that the level spacing distribution for the quantum system is well approximated by the Berry-Robnik-Brody distribution, and accordingly the classical limit displays mixed dynamics.     

Canonical realizations of the lie algebras gl(n, R) and sl(n, R) I. Formulae and classification

The generators of the Lie algebra of the general linear group GL(n, R) and of the special linear group SL(n, R) are, recurrently, expressed through polynomials in the quantum canonical variables p_t and q_t. These realizations are skew-Hermitian, the Casimir operations are realized by constant multiples of identity element and, in dependence on the number of the canonical pairs used, they depend on d(d?1 for sl (n,R)), d = 2, …, n, free real parameters.     

Mean-field bounds on the magnetization for ferromagnetic spin models

The mean-field approximation is shown to give an upper bound on the magnetization for a large class of one-component models with arbitrary ferromagnetic pair interactions. Specific examples include discrete and continuous spin Ising models. In addition, a new comparison inequality for multicomponent rotators is proven which allows this result to be extended to the plane rotator and classical Heisenberg ferromagnets.     

On representations of the groups Sp(n, 1) and Sp(n)

New classes of unitary irreducible representations of Sp(n, 1) which can be useful for applications in physics are obtained. The infinitesimal operators of these representations of Sp(n, 1) and of irreducible representations of Sp(n+1) with highest weights (m, m, m₃,…,m_n+1) and (m₁, m₂, 0,…,0) are expressed in terms of the simple Clebsch–Gordancoefficients for Sp(n). For Sp(3) and Sp(2, 1) they are found in an explicit form.     

High-temperature expansion of surface critical exponents for the classical n-vector model

The surface critical exponents of the classical n-vector model are investigated in the high-temperature series expansion. The first nine coefficients of the layer susceptibility for the semi-infinite simple cubic lattice are presented. The n-dependence of surface exponents is compared with the results of other theories.     

Borel-summability of the high temperature expansion for classical continuous systems

It is shown that for classical gases with stable, bounded and absolutely integrable pair interactions, the Taylor expansions in of the correlation functions and the pressure are Borel-summable at =0.     

On a resolution of the multiplicity problem for U(n)

The Borel-Weil theory of holomorphic induction is used to provide a resolution of the multiplicity problem occuring in the tensor product decomposition of representations of the U(n) groups.     

Oscillator strengths for 3dn4s → 3dn4p transitions in the iron series

The observed oscillator strengths for the 3dⁿ4s → 3dⁿ4p transitions in the iron series show anomalous behaviour for Cr and Mn : the former is exceedingly small whereas the latter is unusually large.Theoretical Hartree-Fock gf-values are reported and a considerable discrepancy with experimental values is noted for Cr. The effect of the interaction of 3dⁿ4p with 3d^n?14s4p is studied using a fixed core, multi-configuration Hartree-Fock approximation. This interaction does not improve significantly the agreement with observed values.