Spin anisotropy effects on the dimerization of the magnetostrictive quasi-one-dimensional XY model

The one-dimensional first-neighbour spin - $\text{1}\text{2}$ magnetostrictive XY model (with crystalline degrees of freedom assumed three- dimensional) with $\text{different}$ X and Y spin coupling constants presents a quite rich spin-Peierls dimerization phase diagram. In the (low anisotropy) - (low temperature) region we recover previous results (in particular the possibility for a first-order phase transition in the absence of external magnetic field); in the other three regions of the temperature-anisotropy space interesting branches of the phase diagram (including the tricritical line) are exhibited (for the first time as far as we know).     

Spin and isospin in a gauge theory with monopoles

The mechanism by which systems of spinless bosons with isospin and spinless magnetic monopoles acquire a spin in their ground states is investigated in the context of SU(2) gauge models. Contrary to recent claims, it is demonstrated that isospin degrees of freedom are not converted into spin degrees of freedom. For a spin $\text{1}\text{2}$ state, solutions are explicitly constructed, exhibiting the isospin degree of freedom.     

Analysis of the two-state model and its application for amorphous iron alloys

The magnetic phase diagram for the two-state Weiss model is calculated in the mean field approximation (MFA) for low spin S₀ = $\text{1}\text{2}$ and high spin S₁ = $\text{3}\text{2}$. We show that the two-state model together with the assumption of the strong shor t range order (SRO) can account for the observed Curie temperature data in amorphous Fe_1-xA_x (A = B, Hf, Ti, Zr) alloys.     

Determination by polarization analysis of the scattering amplitudes a+ and a- and of the degree of orientation of nuclei polarized by hyperfine fields in magnetically ordered substances

Improvements of the Ito-Shull techniques are suggested for measuring the scattering amplitudes a₊ and a_- associated with the compound states $\text{I +}\text{1}\text{2}$ and $\text{I -}\text{1}\text{2}$ which are formed by the nucleus of spin I and the incident neutron. In ferro- and ferri-magnets one can increase the sensitivity by suppressing the electronic part of the magnetic scattering when polarizing the neutrons along the scattering vector. In anti-ferromagnets one can separate the nuclear magnetic part by substracting the electronic magnetic scattering with unpolarized neutrons from the total magnetic scattering (electronic + nuclear) obtained by measuring the spin-flip amplitudes U^+- or U^-+.     

Evidence for a modulated ordering in CeB6 due to the Kondo effect

Neutron diffraction experiments have been performed on CeB₆ single crystals to investigate the magnetic order in zero field. CeB₆ orders anti-ferromagnetically below T_N = 2.8 ± 0.1 K with a second order phase transition. The magnetic order is defined by the two wave vectors $\text{k}{}_1\text{= 〈}\text{1}\text{4}\text{1}\text{4}\text{0〉}$ and $\text{k}{}_2\text{= 〈}\text{1}\text{4}\text{1}\text{4}\text{1}\text{2}\text{〉}$. No magnetic intensity anomaly has been detected at the transition between the phases II and III. This transition is quite original and corresponds only to a phase shift of the modulation. This unusual behaviour can be understood if the effective Kondo effect is the same in both phases. The structure of the low temperature phase III is probably a helical order in (001) planes with moments along the fourfold axes in constrast with the crystal field anisotropy. In phase III there is a homogeneous moment reduction due to the Kondo effect whereas in the phase II it is non-homogeneous with a sequence (+ μ0 - μ0) containing non-magnetic planes.     

A hamiltonian with broken supersymmetry for the xenon isotopes

A hamiltonian with broken $\text{u}\text{(}\text{6}\text{2}\text{j+1)}$ supersymmetry is proposed that can describe collective excitations in nuclei with high-spin, single-j orbitals. Its bosonic part is identical with IBA, while the fermionic degrees of freedom, are characterized by the seniority quantum number. The ground state as well as excited energies of eight xenon isotopes with both odd and even mass are fairly well described by the so(6) limit of this hamiltonian with only one set of parameters.     

Finite size scaling and low mass glueballs

We propose finite lattice effects as a probe of the glueball mass spectrum, and give an analysis of the recent SU(2) Monte Carlo data of Brower, Nauenberg and Schalk in terms of a gas of free glueballs. For L⁴ lattices with L = 4, 5, 6 fits are made to ξ(m = 1/aξ) which indicate a rather large effective number of degrees of freedom (i.e. statistical degeneracy where a spin J counts as 2J + 1) from 5 to 15 states. As the degeneracy is increased, the central glueball mass increases from $\text{m = (1.3±0.2)}\text{κ}$ at degeneracy 5 to about $\text{m = (1.9±0.2)}\text{κ}$ at degeneracy 15, relative to the SU(2) string tension $\text{κ}$.     

Dimerization in the magnetostrictive one-dimensional XY model

We discuss the one-dimensional first-neighbor $\text{1}\text{2}$-spin magnetostrictive XY model (where the crystalline degrees of freedom are assumed to be three- dimensional), and exhibit that, for all temperatures below T_c, no other contributions to the structural order appear than the pure dimerization one. The influences of temperature and elastic constant on the order parameter and sound velocity are analyzed as well.     

Classical behaviour of the soliton density in Rb2ZnCl4 studied by 87Rb NMR

The temperature dependence of the soliton density n_s(T) which has been studied in Rb₂ZnCl₄ by ⁸⁷Rb NMR could be fitted to a classical formula using only one fit parameter. From our data we cannot confirm recent experimental results which yield a critical exponent $\text{1}\text{2}$ for the soliton density. The results are discussed with respect to the free energy where the soliton density acts as the order parameter. Moreover, couplings to other degrees of freedom, e.g. the elastic strains, are considered.     

N2 Monolayers on graphite: Specific heat and vapor pressure measurements — thermodynamics of size effects and steric factors

Calorimetric and vapor pressure measurements of N₂ monolayers on Grafoil have been made in the regions recently explored by neutron scattering. The phase transition at T = 48 K involves approximately symmetric specific heat anomalies of 2̃ K FWHM, and the peak position shifts about 1 K from $\text{1}\text{3}$ to $\text{2}\text{3}$ of one monolayer. In spite of the peak width and temperature shift the transition is intrinsically first order, due to melting of the √3 registered structure into a disordered phase in the presence of 2D vapor. The shift and broadening are shown to be a consequence of size effects primarily due to large edge-to-area ratios of the ordered phase domains. A formula relating the domain size to the shift in transition temperature gives r = 50' A for the mean radius of the domains. At film densities above $\text{2}\text{3}$ monolayer the peak broadens and shifts to a higher temperature until a critical region is reached near T= 85 K. The combined heat capacity and vapor pressure data indicate that there is no two phase region at coverages near monolayer completion and that the transition near T = 85 K is higher than first order. Effects of molecular orientation and surface-normal vibration appear in certain regions of temperature and density. A phase diagram is constructed which is consistent with both calorimetric and neutron scattering results.     

The quantum mechanical toda lattice

The aim of this paper is to establish the exact quantization conditions for the three-body Toda lattice. The Hamiltonian consists of the kinetic energy for three particles in one dimension, and of the potential energy which couples each particle to its two companions through an exponential spring. After eliminating the center of mass motion, one is left with a system of two degrees of freedom and two constants of motion, the total energy E and a third integral A which commute. Nevertheless, no transformation has been found to separate the classical equations of motion or Schrödinger's equation. The wave function is written as a double Laurent series. Its coefficients have to satisfy two sets of recursion relations on a triangular grid where each set insures that we have a simultaneous eigenfunction of E and A. The condition for the convergence of this series can be expressed as the vanishing of a tridiagonal infinite determinant with 1 in the diagonal and the inverse of a third-order polynomial in the first off-diagonals. The coefficients in this polynomial are E and A, and the variable corresponds to a component of the wave vector associated with the wave function. This determinant can be treated exactly as Hill's, and yields the 3 components. The condition for the square integrability of the wave function requires the phase angle of the principal minors to be equal to 0, $\text{π}\text{3}$, or $\text{2π}\text{3}$ according as the representation of the cyclic groups, for each component of the wave vector. But the third condition follows from the two others. The analogy with the corresponding two-body problem is pointed out.     

Heat capacity of a five-coordinated iron(III) complex,chlorobis(N,N-dimethyldithiocarbamato) iron(III), between 0.4 and 300 k: New finding of a magnetic phase transition

The heat capacity of the title complex, Fe[S₂CN(CH₃)₂]₂Cl, has been measured between 0.4 and 300 K. A λ -type phase transition with a small shoulder arising from magnetic ordering was found at (0.609 ± 0.005) K. The character of the ordered phase has been suggested to be ferromagnetic on the basis of comparison between the methyl- and ethyl-homologues. The magnetic hyperfine structure of the Mössbauer spectra and the line broadening due to electronic relaxation effects at 1.2 K hitherto reported are concluded to result from a critical slowing-down when the magnetic transition temperature is approached from the high-temperature side. A Schottky-type anomaly arising from the zero-field splitting of a single ferric ion was observed around 2 K. The excess entropy beyond the lattice contribution at low temperatures amounts to (14.05 ±0.27) J K^?1mol^?1, which cannot be accounted for solely by the magnetic entropy of Rln 4 (= 11.53 JK^?1mol^?1) for the intermediate spin of $\text{S =}\text{3}\text{2}$. Two possibilities concerning additional conntribution have been discussed; one is a mixing of spin species of $\text{S =}\text{5}\text{2}$ and the other is a tunnel-splitting of the rotational levels of four methyl-constituents. The present study cannot give a definite conclusion as to the existence of dimeric units suggested from Mössbauer spectroscopy.     

Splitting the degeneracy of harmonically-bound identical spinless bosons: General derivation

The Gartenhaus-Schwartz model of N particles interacting via pairwise harmonic potentials $\text{V}{}_{\mathrm{ij}}\text{=}\text{1}\text{2}\text{kR}{}_{\mathrm{ij}}{}^2$ is extended by addition of an arbitrary pairwise interaction small enough to be treated by degenerate perturbation theory. The theory is worked out for a rarefied fluid of N spinless bosons, to give the splittings of the degeneracies of the U(3N?3) symmetry inherent in the Gartenhaus-Schwartz model. Following Moshinsky and Kramer the external field is formally introduced in order to reduce the zeroth-order problem to the 3N-dimensional harmonic oscillator. For systems with more particles than quanta, a recipe is given to construct states in which all the excitation is in internal degrees of freedom and none is in translation. Analytical solutions are obtained for states with no more than two quanta in excitation of relative motion of any one pair of particles.     

Absence of the second-order phase transitions in the dimerized Ising chains with spin larger than 12

A general spin S Ising chain interacting with a single phonon mode of the harmonic lattice is studied. The thermodynamics of the spin system is calculated exactly for S = 1, $\text{1}\text{2}$ and $\text{3}\text{2}$, while self-consistent equations for the induced lattice distortions are derived. It is demonstrated that for S >$\text{1}\text{2}$ there is no second-order phase transition, in contrast to the case S = $\text{1}\text{2}$ which was proved to have a tricritical point. This is found to cohere with the previous studies of the dimerized magnetic model chains.     

Magnetic moments of composite fermions

There have been a considerable number of papers proposing composite models for leptons and quarks. Recently, Glück and Lipkin have stated that reproducing the observed magnetic moments of these fermions presents a serious difficulty for these composite models. We show for a renormalizable theory that, in contrast to Glück's and Lipkin's nonrelativistic arguments, a deeply bound system (with heavy constituent particle masses m_c) of (total) spin $\text{1}\text{2}$, charge e and mass m has the magnetic moment $\text{(e/2m) [1 +}\text{“usual” (QED + QCD + weak) corrections +O}\text{(m/m}{}_{\mathrm{<mtext>c</mtext>}}\text{)}\text{“new” bindng corrections]}$. Although there remains the considerable dynamical problem of obtaining “light” bound fermions from heavy constituents, there is no separate, additional magnetic moment difficulty.     

Proprietes magnetiques et etude par effet Mössbauer du thiosilicate Fe2SiS4

Fe₂SiS₄$\text{(a = 12,407}\text{A}\text{?}\text{, b = 7,198}\text{A}\text{?}\text{, c = 5,812}\text{A}\text{?}$, space group Pnma) has the olivine structure; the ferrous ions are located in two kinds of sites: one half in planes of mirror symmetry m, the other half in centers of symmetry. 1?.The magnetic study of this compound by means of magnetization measurements and Mössbauer effect, indicates from 127 K an antiferromagnetic arrangement along oy for the m sites, and an induced partial order of the same kind for the 1? sites. At 33 K, the Fe²⁺ spins in 1? sites are completely ordered and at the same time takes place a rearrangement of the magnetic structure. The observed complex model is analogous to that of Fe₂GeS₄, i.e. antiferromagnetic along 0x and ferrimagnetic along Oz.     

The antiferromagnetic structures of TbCu2Ge2 and HoCu2Ge2 by neutron diffraction

The magnetic structures of TbCu₂Ge₂ and HoCu₂Ge₂ were studied by neutron diffraction. At 293 K the chemical structure is tetragonal body centered, space group I 4/mmm. The magnetic cell at 4.2 K is four times larger than the chemical one with a wave vector $\text{k =}\text{1}\text{2}\text{0}\text{1}\text{2}$. The magnetic space group is triclinic P_a$\text{1}$(Sh₂⁷) for both compounds. The moment values and directions are μ_Tb = 8.48(6) [μ_B] along [110] tetr. and μ_HO = 6.5(1)[μ_B] making an angle of 81.4(°) with c and 80(°) with a₁. The structure consists of ferromagnetic (101) layers stacked antiferromagnetically.     

1616 supergravity coupled to matter: The low energy limit of the superstring

We analyze irreducible, N = 1 supergravity theories with 16 fermionic degrees of freedom. The lagrangians for pure $\text{16}\text{16}$ supergravity, and for $\text{16}\text{16}$ supergravity coupled to arbitrary chiral superfields are constructed. These theories are shown to have natural SU(1,1) non-compact symmetry. The low energy field theory limit of the superstring is conjectured to be of this type.