A new model for the ground-state spin determination in ferromagnetics: The influence of many-electron exchange effects on the ground-state total spin in titanium and nickel

A new approximate exchange interaction operator, derived from the exact atomic second quantization formalism, has been applied to the study of the magnetic properties of atoms with spin $\text{S =}\text{1}\text{2}$ and S = 1 which obey Hund's rule. The new operator involves the effects of one-pair and two-pair electron exchanges. The one-pair exchange effects are compared with the Heisenberg model. It is shown that our model comprises the symmetry properties of the atomic wavefunction and the interaction of all electrons in the unfilled shells of two atoms, which are not considered in the Heisenberg theory. The conditions under which the new one-pair exchange effect may be used to improve the old one are pointed out. The significance of the two-pair exchange effects is discussed. It is demonstrated that, owing to the simultaneous exchange of two electron pairs, the total ground-state spin of two atoms may have intermediate values in addition to those predicted by the Heisenberg model. The importance of the interrelation between the first- and second-order effects, with respect to both sign and magnitude, is pointed out. The existence of the intermediate values, even in the case where the first order exchange integral is negative, is taken as a conjecture by which one may explain the fact that the mean magnetic moment per atom in magnetic 3d metals is not equal to the spin magnetic moment of an individual atom and accounts for the existence of magnetic ordering when the first order exchange integral is negative.     

Energy-weighted sum rules for spin operators and ground-state correlations

Energy-weighted sum rules are obtained for the spin part, both isoscalar and isovector, of the magnetic dipole operator. The same interaction is used to evaluate the relevant double commutator as is used to induce ground-state correlations. First a spin-dependent delta interaction is used; then a tensor interaction is considered. The main point of this work is that there is a lot of energy-weighted strength at high energies.     

Bifurcation in ground-state fidelity for a one-dimensional spin model with competing two-spin and three-spin interactions

A one-dimensional quantum spin model with the competing two-spin and three-spin interactions is investigated in the context of a tensor network algorithm based on the infinite matrix product state representation. The algorithm is an adaptation of Vidal?s infinite time-evolving block decimation algorithm to a translation-invariant one-dimensional lattice spin system involving three-spin interactions. The ground-state fidelity per lattice site is computed, and its bifurcation is unveiled, for a few selected values of the coupling constants. We succeed in identifying critical points and deriving local order parameters to characterize different phases in the conventional Ginzburg-Landau-Wilson paradigm.     

A direct determination of the nuclear ground-state spin of156Eu

The nuclear ground-state spin of the doubly-odd nucleus¹⁵⁶Eu has been measured directly using ABMR techniques to be I=0, thus distinguishing between the contradicting results obtained in beta-decay and nuclear orientation measurements.     

A model for ground-state and excited-state microwave optical double resonance

A model is developed to describe the physical principles of both ground-state and excited-state microwave optical double resonance. This model uses a steady-state kinetic analysis to determine the populations of three quantum levels in the presence of two monochromatic radiation fields. The microwave transition rate and the laser transition rate are obtained from separate analyses using the semiclassical two-state transition probability averaged over the effects of collisions. The Doppler effect of the optical transition rate is explicitly included. The competing effects of laser power, microwave power, and pressure on signal intensity and lineshape are described. Calculated lineshapes and relative signal intensities based on this model are in good agreement with previous measurements on BaO and NO₂.     

Hyperspherical harmonic model for the ground-state baryons

The wave functions of the 18 ground-state light baryons are calculated in the quark model. The space wave functions are obtained by means of a (confining) hyperspherical harmonic potential in a nonrelativistic Hamiltonian. The different flavors (up, down, strange) are treated as identical particles.     

A general method for constructing vector integrable lattice systems

A method for generating vector-value integrable analogies of integrable lattice systems or integrable differential-difference equations is presented. The basic ingredient of the method is to insert permutation matrices. We formulate the zero-curvature representations and Hamiltonian structures of the resulting vector lattice systems. The effectiveness of the method is illustrated using some examples such as the Volterra lattice, the Belov–Chaltikian lattice, the Ablowitz–Ladik lattice and the Heisenberg ferromagnet lattice.     

A spin model for cholesteric liquid crystals

A spin model for cholestric liquid crystals is presented. The free energy is obtained in the mean field and from that the director correlation functions. It is found that one of the correlation functions diverges as (k₃² + bk_⊥⁴)^?1 where k₃ is the component of the wave-number parallel to the pitch axis, x_⊥ the component perpendicular to the pitch axis and b is a constant. This divergence persists to all orders in the small parameter q₀a where a is a molecular length and q₀ is 2π over the pitch. This divergence implies that the cholesteric state is unstable with respect to fluctuations.     

A model for strongly coupled spin waves

The connection between a model of coupled oscillators and the system of coupled spin waves is discussed. Also the region ofk-space is estimated in which the spin-wave amplitudes have appreciable magnitude when a normal mode of coupled spin waves is excited.     

How to evaluate ground-state landscapes of spin glasses thermodynamical correctly

Ground states of three-dimensional Ising spin glasses are calculated for sizes up to 14³ using a combination of a genetic algorithm and cluster-exact approximation. For each realization several independent ground states are obtained. Then, by applying ballistic search and T=0Monte-Carlo simulations, it is ensured that each ground state appears with the same probability. Consequently, the results represent the true T=0 thermodynamic behavior. The distribution P(|q|) of overlaps is evaluated. For increasing size the width of P(|q|) and the fraction of the distribution below converge to zero. This indicates that for the infinite system P(|q|) is a delta function, in contrast to previous results. Thus, the ground-state behavior is dominated by few large clusters of similar ground states. Received 17 June 1999     

Non-universality for ising-like spin systems

Renormalisation calculations are carried out which reasonably reproduce the interaction-dependent critical point exponents of the Baxter model. Similar calculations indicate non-universal behaviour of a nearest and next-nearest neighbour pair-interaction Ising model in two dimensions.     

A finite block spin model for permanent magnets

We propose a finite block spin phenomenology for permanent magnets in which we consider an average domain as a block spin. The permanent ferromagnetism arises in two ways: (1) the ferromagnetism that occurs inside a big block spin, i.e. the intrablock ferromagnetism, and the ferromagnetism between small block spins (SBSs) in a big block spin (BBS) which can be induced by collective ferromagnetic pairing between two SBSs mediated by temperature-irreversible bosonic strains; and (2) the ferromagnetism between BBSs, i.e. the interblock ferromagnetism. The coercivity originates from temperature-irreversible strains treated as external phonons.     

A toy model for higher spin Dirac operators

This paper deals with the higher spin Dirac operator Q_2,1 acting on functions taking values in an irreducible representation space for so(m) with highest weight $ (\tfrac{5} {2},\tfrac{3} {2},\tfrac{1} {2},...,\tfrac{1} {2}) $ (\tfrac{5} {2},\tfrac{3} {2},\tfrac{1} {2},...,\tfrac{1} {2}) . This operator acts as a toy model for generalizations of the classical Rarita—Schwinger equations in Clifford analysis. Polynomial null solutions for this operator are studied in particular.     

On ground-state wavefunctions for Sutherland-Calogero systems in an external field

Conditions are considered under which the ground-state wavefunctions of quantum systems of interacting particles in an external field are factorizable and can be found explicitly. The corresponding classical systems of particles are completely integrable; in the quantum case an extra integral of motion is constructed for a two-particle system.     

Quantum-dot ground-state energies and spin polarizations: soft versus hard chaos

We consider how the nature of the dynamics affects ground state properties of ballistic quantum dots. We find that "mesoscopic Stoner fluctuations" that arise from the residual screened Coulomb interaction are very sensitive to the degree of chaos. It leads to ground state energies and spin polarizations whose fluctuations strongly increase as a system becomes less chaotic. The crucial features are illustrated with a model that depends on a parameter that tunes the dynamics from nearly integrable to mostly chaotic.     

Diagonalization-free implementation of spin relaxation theory for large spin systems

The Liouville space spin relaxation theory equations are reformulated in such a way as to avoid the computationally expensive Hamiltonian diagonalization step, replacing it by numerical evaluation of the integrals in the generalized cumulant expansion. The resulting algorithm is particularly useful in the cases where the static part of the Hamiltonian is dominated by interactions other than Zeeman (e.g. in quadrupolar resonance, low-field EPR and Spin Chemistry). When used together with state space restriction tools, the algorithm reported is capable of computing full relaxation superoperators for NMR systems with more than 15 spins.