Search Results (26 total)

We present a measurement of the spin-dependent cross sections for the ³He→(e→,e^′)X reaction in the quasielastic and resonance regions at a four-momentum transfer 0.1≤Q²≤0.9  GeV². The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt-Cottingham and extended Gerasimov-Drell-Hearn sum rules for the first time. The data are also compared to an impulse approximation calculation and an exact three-body Faddeev calculation in the quasielastic region.

The generalized forward spin polarizabilities γ₀ and δ_LT of the neutron have been extracted for the first time in a Q² range from 0.1 to 0.9  GeV². Since γ₀ is sensitive to nucleon resonances and δ_LT is insensitive to the Δ resonance, it is expected that the pair of forward spin polarizabilities should provide benchmark tests of the current understanding of the chiral dynamics of QCD. The new results on δ_LT show significant disagreement with chiral perturbation theory calculations, while the data for γ₀ at low Q² are in good agreement with a next-to-leading-order relativistic baryon chiral perturbation theory calculation. The data show good agreement with the phenomenological MAID model.

We have measured the spin structure functions g₁ and g₂ of ³He in a double-spin experiment by inclusively scattering polarized electrons at energies ranging from 0.862 to 5.058 GeV off a polarized ³He target at a 15.5° scattering angle. Excitation energies covered the resonance and the onset of the deep inelastic regions. We have determined for the first time the Q² evolution of Γ₁(Q²)=∫₀¹g₁(x,Q²)dx, Γ₂(Q²)=∫₀¹g₂(x,Q²)dx, and d₂(Q²)=∫₀¹x²[2g₁(x,Q²)+3g₂(x,Q²)]dx for the neutron in the range 0.1≤Q²≤0.9  GeV² with good precision. Γ₁(Q²) displays a smooth variation from high to low Q². The Burkhardt-Cottingham sum rule holds within uncertainties and d₂ is nonzero over the measured range.

We present data on the inclusive scattering of polarized electrons from a polarized ³He target at energies from 0.862 to 5.06 GeV, obtained at a scattering angle of 15.5°. Our data include measurements from the quasielastic peak, through the nucleon resonance region, and beyond, and were used to determine the virtual photon cross-section difference σ_1/2-σ_3/2. We extract the extended Gerasimov-Drell-Hearn integral for the neutron in the range of four-momentum transfer squared Q² of 0.1–0.9   GeV².

We present an experimental realization of an almost noninvasive stabilization and manipulation method of coexisting and underlying states of pattern forming systems. In a photorefractive single feedback system, a ring control path is used to realize amplitude and phase-sensitive Fourier-plane filtering, utilizing only a few percent of the system's intensity. We were able to stabilize desired but not predominantly excited patterns in parameter space regions where several patterns are present as underlying solutions. By positive (in-phase) and negative (out-of-phase) control, rolls could be excited in parameter regions where hexagonal structures are preferably stable.

Clusters of Lennard-Jones atoms adsorbed on a graphite surface are studied using Monte Carlo simulation. We investigate the stability of registered and nonregistered structures at low temperatures. The model is two dimensional with adatom-adatom interactions specific to krypton, while the amplitude of the hexagonal substrate corrugation potential V₁ is taken as a variable. In order to allow the density to change continuously, free boundaries have been employed. We locate a thermally induced as well as a field induced phase transition in the plane of temperature and corrugation amplitude. The transition is from a modulated (incommensurate) structure at low corrugation amplitude and low temperature to a registered (commensurate) lattice at stronger corrugation and/or higher temperature. We find that free surfaces enhance the stability of the √3 × √3 R30° structure. Our results support the existence of an incommensurate-commensurate transition driven by thermal expansion as proposed by Gordon and Villain [J. Phys. C 18, 3919 (1985)].

The growth of ordered domains in the two-dimensional chiral clock model following a quench from the disordered state to a low-temperature nonequilibrium state is studied by Monte Carlo simulation. The time-dependence of the mean-linear domain size R(t), the excess energy, and the dynamical structure factor is obtained as a function of the asymmetry parameter Δ. In general, periodic boundary conditions are used, but free surfaces are also applied in some cases. The growth exhibits at zero temperature two qualitatively different regimes, depending on Δ. In the dry part of the phase diagram, 0≤Δ≤0.25, the growth is algebraic, R(t)∼tⁿ, whereas it is pinned by vortex configurations in the wet part, Δ>0.25. The vortices cannot be annealed away with the employed updating algorthm. The kinetic exponent n, calculated from R(t) data from a lattice with 240×240 spins varies from 0.35 for Δ=0 to 0.50 for Δ=0.25. n could not be extracted from R(t) data for a smaller lattice with 120×120 spins. In contrast, the growth calculated from the structure factor shows only small finite-size effects. Analysis of the structure factor data leads to an estimate for n consistent with 0.5 for 0≤Δ≤0.25. Quenches to finite temperatures, T≃1/2T_c(Δ), show that temperature excitations can remove the zero-temperature pinning effects and that n is consistent with 0.5 (Δ>0.25). n is temperature independent within statistical error for 0≤Δ≤0.25.

A Monte Carlo renormalization-group scheme based on a ‘‘floating sublattice’’ blocking rule is constructed for the two-dimensional three-state chiral clock model. The presence of a critical phase is established by matching certain wave-vector-dependent correlation functions derived from lattices differing in linear size by a factor of 2. The wave vector, which in a function of temperature and the asymmetry parameter Δ, is determined from the simulations. For Δ=0.45, a critical phase is established in a temperature range. For Δ=0.35, no critical phase is observed, suggesting that the phase diagram has a Lifschitz point in the interval 0.35<Δ<0.45. Alternatively, the wave vector and the width of the critical phase at Δ=0.35 are much smaller than for Δ=0.45..AE

Layers of atoms or molecules adsorbed on surfaces may exhibit floating critical phases. To investigate this phenomenon we have developed a Monte Carlo renormalization-group scheme and performed calculations on the three-state chiral Potts model. The results indicate a continuous transition from a floating phase to a liquid phase at a temperature much higher than that found by series-expansion methods.

Differential (in angle) electron scattering experiments on laser-excited ¹³⁸Ba ¹P were carried out at 30- and 100-eV impact energies. The laser light was linearly polarized and located in the scattering plane. The superelastic scattering signal was measured as a function of polarization direction of the laser light with respect to the scattering plane. It was found at low electron scattering angles that the superelastic scattering signal was asymmetric to reflection of the polarization vector with respect to the scattering plane. This is in contradiction with theoretical predictions. An attempt was made to pinpoint the reason for this observation, and a detailed investigation of the influence of experimental conditions on the superelastic scattering was undertaken. No explanation for the asymmetry has as yet been found.

The Ising model considered by von Boehm and Bak [Phys. Rev. Lett. 42, 122 (1979)] is studied in a spin-½ version with the spins arrayed on a simple cubic lattice. The model is uniaxial with ferromagnetic interaction between nearest-neighbor spins in the xy planes and competing interactions between nearest-neighbor and next-nearest-neighbor spins in the z direction. The phase transitions of the model are studied by mean-field and Monte Carlo calculations for the same set of interaction parameters as chosen by von Boehm and Bak. The mean-field calculations suggest that the wave vector q, as a function of temperature, picks up every rational number from ¼ at low temperature to q₀≃0.3036 at T_N, the transition temperature to the paramagnetic phase. Monte Carlo calculations with periodic boundary conditions are performed on lattices with M×M×L spins with M ranging from 4 to 10. Two values of L, 56 and 280, are considered. The calculations show 4 and 16 sinusoidal phases in the two cases, respectively. The transitions between the ordered phases appear to be first order. The number and value of the wave vectors in the two cases agree with the pattern from the mean-field calculations. Monte Carlo calculations with free surfaces for L=56 lead to a pattern similar to that of the corresponding calculations with periodic boundary conditions. It is argued that the temperature dependence of the wave vector is consistent with the devil's-staircase type of behavior. The values of T_N and q₀ determined from the Monte Carlo calculations are in good agreement with the results of an analysis of the ordering susceptibility obtained from known general series.

The Monte Carlo technique is applied to a study of the phase transitions and the critical behavior of the spin-½ Ising model on an fcc lattice with mixtures of two- (J₂) and four - (J₄) spin interactions. In the limit J₂=0 the model exhibits a first-order transition. The transition remains of first order for J₄/J₂≳1/2, but a crossover to continuous transitions is found around J₄/J₂≈1/4-1/2 indicating that the model exhibits tricritical behavior. A modified mean-field theory is presented leading to an approximate description of the tricritical behavior in agreement with the Monte Carlo calculations. In the region of continuous transitions. 0<~J₄/J₂≲1/4, the critical exponent β pertaining to the order parameter derived from the Monte Carlo data retains the Ising value, in accordance with the universality hypothesis. Our findings show that the four-spin interactions do not lead to nonuniversal critical behavior, contrary to the conclusions made by Griffiths and Wood from a series analysis.

Ising models on fcc lattices with pure three-spin or pure four-spin interactions are shown by Monte Carlo calculations to exhibit only one phase transition which is of first order. The transition temperature of the model with pure four-spin interactions differs from the Onsager result. This implies that the model is likely not to possess a self-dual property as claimed by Wood.

A spin system with truncated secular dipolar coupling is studied by Monte Carlo calculations. The spins are arrayed on a simple-cubic lattice with periodic boundary conditions. The spin system is investigated in three cases corresponding to the magnetic field, B→₀, along the [111] direction at positive spin temperature T and to B→₀ along the directions [110] and [111] at negative T. The ordered spin structures have in all three cases a periodicity of four layers at low values of |T|. The Monte Carlo calculations show in two of the cases that the low-|T| structure is the only ordered phase, and that the transition to the paramagnetic phase is of first order. In the remaining case the Monte Carlo calculations suggest a first-order transition to a sinusoidal phase with a periodicity of five layers. A mean-field calculation indicates that the spin system may actually possess a larger number of stable phases than observed in the Monte Carlo calculations. This is discussed in terms of possible periodic structures in the finite lattice. The results are compared with the results of NMR experiments on the ordered nuclear spin system in CaF₂.

The phase diagram of a model for a uniaxially stressed antiferromagnet of cubic symmetry is calculated using high-temperature series analysis of the ordering susceptibility. It is shown that the model exhibits a bicritical point in zero stress, σ=0, and that the phase diagram includes a spin-flop-like and an antiferromagnetic phase for σ<0 and σ>0, respectively. We have determined the crossover exponent to be φ=1.33±0.10 in agreement with renormalization-group predictions for a n=3 system. The variation of the exponent γ along the phase boundaries separating the ordered phases and the paramagnetic phase is discussed in the context of universality.

A general scheme is presented to calculate high-temperature series coefficients for ensemble averages of spin operators for spin systems with Hamiltonians containing a large number of model parameters. The scheme, which is based on the moment method, provides the series coefficients as exact functions of the model parameters, e.g., spatial dimensionality, coupling distributions in coordinate and spin space, site-dependent field distributions, and spin quantum number. General expressions for the series coefficients for the auto- and pair-correlation functions are given to sixth order in the case of a classical Hamiltonian with bilinear interactions and a one-component site-dependent magnetic field. The general expressions are used to calculate susceptibility series for the simple cubic anisotropic classical Heisenberg antiferromagnet in a uniform nonordering magnetic field along the easy axis. The series coefficients are polynomials in three variables representing the field, the anisotropy, and the ratio of nearest- and next-nearest-neighbor couplings, respectively. From an analysis of the ordering susceptibility series the phase diagram spanned by the temperature and the field has been calculated for various values of the anisotropy parameter. The calculated phase diagram, which includes a spin-flop phase, an antiferromagnetic phase, and a paramagnetic phase, is in agreement with predictions based on Monte Carlo and renormalization-group calculations.

The static properties of a spin system with two species are investigated by the Monte Carlo technique. The Hamiltonian of the system is similar to the effective Hamiltonian describing nuclear spin-spin interactions under the experimental circumstances designed to produce nuclear dipolar magnetic ordering. The spin structures are determined at negative spin temperatures for various ratios, R, of the magnetic moments. The structures are of the antiferromagnetic type. For two values of R we have calculated the temperature variation of the staggered magnetization of the two species as well as components of the bulk and staggered susceptibilities. It is shown that the mean-field theory is qualitatively—but not quantitatively—adequate to describe the transverse and longitudinal bulk susceptibilities for the two species in the antiferromagnetic phase. The results are discussed in relation to recent nuclear-magnetic-resonance experiments on LiF and neutron scattering experiments on LiH.

The internal energy and the order parameter of the three-state Potts model in a simple cubic lattice are calculated using the Monte Carlo technique. Both properties exhibit metastabilities in a small temperature region demonstrating that the phase transition is of first order. This result is in agreement with the prediction of the ε expansion but in contrast to the position-space renormalization-group calculations which lead to a continuous transition.

Certain physical systems are expected classically to exhibit second-order phase transitions but are known to have first-order phase transitions within the renormalization-group approach because no stable fixed point exists. This lack of stable fixed points is caused by fluctuations in the order parameter and depends only upon the symmetry of the system. When a symmetry-breaking field is applied a stable fixed point may emerge and a continuous transition becomes possible. We have studied this crossover from first-order to second-order transitions by three different approaches. Our model has cubic symmetry and the magnetic ground state is similar to that of UO₂ and NdSn₃. Firstly, Monte Carlo calculations confirm the existence of the crossover to a second-order transition in the symmetry-breaking field. A small field does not destroy the first-order transition, and the crossover therefore occurs at a finite field indicating true tricritical behavior. Secondly, the model has been analyzed using high-temperature series for the ordering susceptibility. For large enough fields the analysis suggests a second-order phase transition at a temperature which is the same as that determined from the Monte Carlo calculations. In this field region the series analysis predicts a bicritical point. For small fields the series behave irregularly, which is considered as an indication of a crossover to first-order transitions. Thirdly, a semiquantitative renormalization-group calculation is presented. This calculation supports and explains the tricritical behavior discovered by the Monte Carlo calculation. Related experimental investigations are suggested on UO₂.

The order parameter Φ of the four-dimensional simple hypercubic spin-½ Ising ferromagnet is calculated by the Monte Carlo technique. The data, which may be represented by Φ(t)=B(-t)^1/2|ln(-t)|^1/3 with 1.53<B<1.56 for 0.005<-t≡(T_c-T)/T_c<0.40, supports the theoretical prediction of a multiplicative logarithmic correction to the mean-field description of the critical behavior in four dimensions.

Inelastic and superelastic scattering of 30- and 100-eV electrons by laser-excited 6s6p ¹P and subsequent cascade-populated 6s6p ³P, 6s5d ¹D, and 6s5d ³D Ba atoms have been observed for the first time. Absolute differential cross sections for the singlet and relative scattering intensities for the triplet species have been determined in the 5°-20° angular region. Under the present conditions excitations dominate over de-excitations.

The Monte Carlo technique is used to calculate the static properties of spin systems with an interaction described by a secular dipolar Hamiltonian with a finite range of interaction. The spins are arranged in a simple cubic lattice with periodic boundary conditions. The static spin structures are determined for the magnetic field along the three directions [001], [110], and [111], both at positive and at negative spin temperatures. The spin structures, which are of antiferromagnetic type, are compared to predictions based on the mean-field theory and to NMR experiments on CaF₂. Two of the antiferromagnetic spin systems are investigated in detail and the following properties are calculated: the critical temperature, spontaneous sublattice magnetization, internal energy, heat capacity, bulk and staggered susceptibilities, and pair- and autocorrelation functions. Series expansions of a number of properties in the paramagnetic phase support the results of the Monte Carlo calculations. The Monte Carlo data are used to derive the critical exponents and critical amplitudes for the spontaneous sublattice magnetization, longitudinal staggered susceptibility, and inverse correlation length. The critical parameters for the two antiferromagnets are discussed within the concepts of the static scaling and universality hypotheses. The parameters are consistent with the classification of the antiferromagnets within the universality class of the three-dimensional Ising model.

The critical behavior of a three-dimensional antiferromagnet described by a six-dimensional order parameter has been investigated by the Monte Carlo technique. A first-order phase transition is observed. This result is in agreement with the prediction of renormalization-group calculations in 4-ε dimensions and with neutron scattering experiments on UO₂, but in contrast to the mean-field theory, which leads to a second-order phase transition.

Molecular-dynamics calculations have been performed on the auto- and pair time-correlation functions in a rigid lattice of magnetic dipoles coupled by a truncated dipolar interaction. The first six terms of the exact time expansion of the correlation functions calculated from first principles are also presented. The analytical forms of the autocorrelation functions are examined and compared to the predictions from a stochastic local-field model due to Kubo and Toyabe. The correlation functions are also used to probe the applicability of a theory of Blume and Hubbard to dipolar coupled spins. Generally, this theory describes the longitudinal dynamics rather well, whereas the transverse dynamics is less satisfactorily described.

Analytical expressions for the sixth and eighth moments of the magnetic-resonance lines of a dipolar-coupled rigid lattice are obtained by performing the commutations of angular momentum operators and the necessary reductions by means of a computer. The expressions are used to derive numerical values of the moments for a simple cubic lattice for varying numbers of interacting neighbors. The sixth and eighth moments predicted from Abragam's trial function for the free-induction-decay curve are compared to the corresponding exact moments reported here. We also present a straightforward method for the algebraic computer calculation of traces of angular momentum operators.