Showing papers on "Spin-½ published in 1979"

Ground state of a spin-½ charged particle in a two-dimensional magnetic field

Abstract: We prove that a spin-\textonehalf{} charged particle moving in a plane under the influence of a perpendicular magnetic field has ($N\ensuremath{-}1$) zero-energy states, where $N$ is the closest integer to the total flux in units of the flux quantum. The ($N\ensuremath{-}1$) independent wave functions are calculated explicitly. The result, which is extremely simple to prove, is an example of the Atiyah-Singer index theorem when applied to the Euclidean two-dimensional Dirac equation.

Single-Site Functional-Integral Approach to Itinerant-Electron Ferromagnetism

Abstract: Itinerant-electron ferromagnetism at finite temperatures is discussed by using the functional-integral method with two fields within the static and saddle-point approximations combined with the single-site approximation; a single atom of a pure metal is regarded as an impurity embedded in the host which is treated by a kind of the alloy-analogy approximation. The amplitude of the local magnetic moment is shown to have a weak temperature dependence and to remain finite even in the paramagnetic state, where the spin susceptibility obeys an approximate Curie-Weiss law. Numerical calculations are made with the use of a simplified model for the density of states of bcc transition metals. Calculated results are discussed with reference to experimental data of iron.

Relativistic Particle Physics

Abstract: 1 One-Particle Problems.- 2 Two-Particle Problems.- 3 Radiation and Quantum Electrodynamics.- 4 The Particle Zoo.- 5 Weak Interactions.- 6 Analyticity and Strong Interactions.- 7 Particular Hadronic Processes.- 8 Particular Electromagnetic Processes in Collisions with Atoms and Nuclei.- Appendices.- A Some Formulas for Partial Waves and Fermions.- A-1 Spherical Bessel, Neuman and Hankel Functions.- A-2 Coulomb Wave Functions.- A-3 Reduction of Dirac Matrices.- A-4 Fermion Spin Summation.- B-1 Unitary Matrices and Their Representations.- B-2 Schur's Lemma and Orthogonality Relations.- B-4 Calculation of the d-Functions.- C Units and Particle Tables.- C-1 Units and Fundamental Constants and Table of Leptons.- C-2 The Pseudoscalar Mesons.- C-3 The Vector Mesons.- C-4 The Baryon Octet.- C-5 The Baryon Decuplet.- C-6 The Tensor Mesons.- C-7 The New Bosons.- References.

New theory of the spin-peierls transition with special relevance to the experiments on TTFCuBDT

Abstract: A new theory of the spin-Peierls transition in spin-1/2 Heisenberg chains is developed in which the phonons are treated in a mean field, random phase approximation as in previous work, but in which the relevant response functions of the spins are calculated using the procedure of Luther and Peschel. 7 This gives a much better approximation than the Hartree treatment used before, taking realistically into account the one-dimensional nature and showing the important differences from an XY model.The leading divergences of the spin response should be given exactly by our calculation. We find a new linear dependence of the transition temperature of the spin-phonon coupling constant and an enhancement of the transition temperature and also of the phonon softening above this temperature. Predictions of some other signatures of the transition, such as the specific heat jump to normal specific heat ratio, are not much changed from earlier work, however. New exact results are found at zero temperature.

Zero-temperature renormalization method for quantum systems. I. Ising model in a transverse field in one dimension

Abstract: A zero-temperature real-space renormalization-group method is presented and applied to the quantum Ising model with a transverse field in one dimension. The transition between the low-field and high-field regimes is studied. Magnetization components, spin correlation functions, and critical exponents are derived and checked against the exact results. It is shown that increasing the size of the blocks in the iterative procedure yields more accurate results, especially for the critical ''magnetic'' exponents near the transition.

Nuclear magnetic relaxation of spin 5/2 and spin 7/2 nuclei including the effects of chemical exchange

Abstract: An equation describing the multiexponential longitudinal and transverse relaxation of quadrupolar nuclei, including the effects of chemical exchange in the limit of fast exchange, is derived. It is difficult to produce analytical solutions for nuclei with spins greater than 3/2, but the equation is in a form convenient for numerical solution, and such solutions are presented for both the longitudinal and transverse relaxation of nuclei with spins 5/2 and 7/2 in the absence of chemical exchange, and for the case of two‐site exchange where one site is in the extreme narrowing limit. Longitudinal relaxation may be described approximately by a single exponential in all cases. However, the transverse relaxation generally must be described as the sum of three and four exponentials for the spin 5/2 and spin 7/2 cases, respectively, the amplitudes of which vary with the correlation time in the absence of exchange, and also with the ratio of the lifetimes of the nucleus in each state when two‐site exchange is considered.

One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature

Abstract: We compute exactly the one particle reduced density matrix ρ (r) of a system of impenetrable bosons in one dimension at zero temperature. We do this by relating ρ (r) to a certain double scaling limit of the transverse correlation function of the one‐dimensional spin 1/2 X–Y model. We study the asymptotic behavior of ρ (r) for large r. This expansion contains oscillatory terms which arise due to the intrinsic quantum mechanical nature of the problem. We use these results to discuss the analytic structure of the momentum density function n (k).

Quantum numbers for Dirac spinor fields on a curved space-time

Abstract: The most general first-order differential operator that commutes with the Dirac operator and hence permits the construction of quantum numbers is given. Necessary and sufficient conditions for its existence are expressed in terms of the generalized Killing tensors of Yano. As a special case we obtain an extension to curved space-time of a covariant description of spin.

Scaling, equation of state, and the instability of the spin-glass phase

Abstract: The free energy and equation of state for the Ising-type random-bond spin-glass are generated in $6\ensuremath{-}\ensuremath{\epsilon}$ dimensions with the aid of renormalization-group recursion relations. Scaling predictions based on previous renormalization-group work are borne out. The specific heat is found to be smooth with a rounded peak above the transition temperature, and the order-parameter exponent $\ensuremath{\beta}$ is greater than 1. We also find, however, that the spin-glass phase is unstable in that certain fluctuations have a negative gap. This instability leads immediately to the nonphysical prediction that the bond average of the square of a spin correlation function is negative. We conclude that there is a serious flaw in current approaches to the spin-glass phase based on the Edwards-Anderson order parameter.

Internal field distributions in model spin glasses

Abstract: The zero temperature probability distribution P(h) of internal magnetic fields is studied, both in the Sherrington-Kirkpatrick random Ising model of a spin glass and in its natural extension to classical vector spins. Theoretical predictions and computer simulations agree that P(h) is linear for small h in the Ising case, and has a hole-P(h)=0 for h< eta -in the vector spin case.

Role of Spin Fluctuations in the Superconductors Nb and V

Abstract: This paper reports investigation of the role of spin fluctuations (paramagnons) in the superconductors Nb and V. For this purpose, experimental data on specific heat and magnetic susceptibility are reanalyzed. Furthermore, the Eliashberg equations including the particle-hole $t$ matrix are solved numerically. It is found that in Nb and V, spin fluctuations substantially reduce ${T}_{c}$, while their contribution to the mass enhancement $\frac{{m}^{*}}{m}$ is typically of order 0.2.

Effect of magnetic fields on a spin-Peierls transition

Abstract: The effect of a magnetic field on the transition temperature of a spin-Peierls transition and the wave vector of the lattice distortion is calculated using the theory based on the Luther-Peschel-type treatment of the spin-correlation functions. Comparison with experiment offers the prospect of testing the predictions of this theory. A brief discussion of the nature of the commensurate to incommensurate transition is included.