Phase Diagram and Structure of the Ground State of the Antiferromagnetic Ising Model on a Body-Centered Cubic Lattice

The Monte Carlo method has been used to study phase transitions and the structure of the ground state of the antiferromagnetic Ising model on a body-centered cubic lattice taking into account the interactions of nearest and next nearest neighbors. All possible magnetic structures of the ground state have been obtained for the first time as a function of the ratio of exchange interactions r. It is shown that six different orderings in the ground state are possible in the system as a function of the r value. The phase diagram of the dependence of the critical temperature on the interaction of the next nearest neighbors is constructed. For the first time, a narrow region (2/3 < r ≤ 0.75) is found in the diagram where the transition from the antiferromagnetic phase to the paramagnetic phase occurs as a first-order phase transition. It is shown that the competition between exchange interactions at the value r = 2/3 does not lead to the frustration and degeneracy of the ground state.     

Theory of surface atom mean square displacements in chromium

The temperature dependence of the mean square displacements for atoms on the (100) and (110) surfaces of chromium has been studied theoretically using the harmonic approximation. Calculations were carried out for crystals with periodic boundary conditions in two directions and free boundary conditions in the third direction using a Born-van Karman model with central interactions up to third nearest neighbors and non-central angular stiffness interaction between nearest and next nearest neighbors. The values of the force constants were chosen to give good fits to the elastic constants and to the bulk phonon dispersion curves in the three major directions [100], [110] and [111]. The ratio of the mean-square displacements at a surface to that in the bulk was calculated as a function of temperature for both the (100) and (110) surfaces. The theoretical, results are compared with the available experimental data from low-energy electron diffraction.     

Au-Ni弱铁磁合金的自发磁矩和居里点

x=0.42—0.55的Au_1-xNi_x晶态合金是从液态直接淬火到室温,测量低温下这些合金的磁化曲线(2—70kOe),得到在温度1.5K下的自发磁矩值,并用Arrott-Noakes图线方法确定居里点。首先用Perrier等人提出的最近邻模型计算平均磁矩,和实验结果进行了比较。并提出最及次近邻模型,即考虑到次近邻的影响,假设一个Ni原子的最、次近邻18个原子有11个以上是Ni原子,它就具有和纯Ni一样的磁矩(0.606μ_B),否则磁矩为零,由此模型计算的平均磁矩值和实验结果比较符合。本文还对合金中自旋集团(spincluster)的存在和自旅集团之间的相互作用作了讨论,给出了表示自旋集团之间铁磁相互作用的平均内场μ_BH/k_B的值。 关键词：     

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice with allowance for intralayer next nearest neighbor interactions have been studied using the replica Monte Carlo algorithm. The character of phase transitions has been analyzed using the histogram method and the Binder cumulant method. It has been found that a transition from the collinear to paramagnetic phase in the model under study occurs as a second order phase transition. The statistical critical exponents of the specific heat α, susceptibility γ, order parameter β, and correlation radius ν, as well as the Fisher index η, have been calculated using the finite-size scaling theory. It has been shown that the three-dimensional Heisenberg model on the layered cubic lattice with allowance for the next nearest neighbor interaction belongs to the same universality class of the critical behavior as the antiferromagnetic Heisenberg model on a layered triangular lattice.     

Higher order elastic constants of alkali halides

The Coulomb, van der Waals and repulsive lattice sums occurring in the higher order elastic constants up to sixth order have been calculated for the rocksalt and cesium chloride structures. Numerical values of the static elastic constants up to sixth order based on a rigid ion model with van der Waals and Born-Mayer type central force interaction between first and second nearest neighbors are calculated for several alkali halides representing both structure types. Fair agreement with the available experimental third and fourth order elastic constant data is found.     

Atomic displacements due to interstitial hydrogen in Cu and Pd

The density functional theory (DFT) is used to study the atomic interactions in transition metal-based interstitial alloys. The strain field is calculated in the discrete lattice model using Kanzaki method. The total energy and hence atomic forces between interstitial hydrogen and transition metal hosts are calculated using DFT. The norm-conserving pseudopotentials for H, Cu and Pd are generated self-consistently. The dynamical matrices are evaluated considering interaction up to first nearest neighbors whereas impurity-induced forces are calculated with M₃₂H shell (where M = Cu and Pd). The atomic displacements produced by interstitial hydrogen at the octahedral site in Cu and Pd show displacements of 7.36% and 4.3% of the first nearest neighbors respectively. Both Cu and Pd lattices show lattice expansion due to the presence of hydrogen and the obtained average lattice expansion ΔV/V = 0.177 for Cu and 0.145 for Pd.      

Nonadiabatic effects in the lattice dynamics of compressed rare-gas crystals

Electron-ion contributions to the energy of rare-gas crystals are discussed from first principles in the framework of the Tolpygo model and its variants. The frequencies of phonons in a neon crystal at pressures p ≠ 0 are calculated in terms of models that go beyond the scope of the adiabatic approximation. Analysis of the contributions from different interactions to the lattice dynamics of the crystals demonstrates that the phonon frequencies calculated in the framework of the simplest model (allowing only for the nearest neighbors) and the most complex model (with the inclusion of the nearest neighbors, next-nearest neighbors, nonadiabatic effects, etc.) for small wave vectors are close to each other. The difference between the phonon frequencies calculated within the above models is most pronounced at the Brillouin zone boundary. Under strong compression, the phonon spectrum along the Δ direction is distorted and the longitudinal mode is softened as a result of the electron-phonon interaction. The contribution from terms of higher orders in the overlap integral S at p ≠ 0 to the phonon frequencies is more significant than that obtained in the band-structure calculations of the neon crystal.     

LATTICE DYNAMICS OF WURTZITE SEMICONDUCTORS GaN AND AlN

The lattice dynamics of wurtzite GaN and AlN is studied within the framework of a rigid-ion model. Short-range interactions up to the third nearest neighbors are described by using a valence-force-field potential and the long-range Coulomb interactions between ions are calculated via an Ewald summation. Phonon dispersion curves, density of states and specific heats are presented.     

Adatom diffusion on a square lattice. Theoretical and numerical studies

A two-dimensional lattice-gas model with square symmetry is investigated by using the real-space renormalization group (RSRG) approach with blocks of different size and symmetries. It has been shown that the precision of the method depends strongly not only on the number of sites in the block but also on its symmetry. In general, the accuracy of the method increases with the number of sites in the block. The minimal relative error in determining the critical values of the interaction parameters is equal to . Using the RSRG method, we have explored phase diagrams of both a two-dimensional Ising spin model and of a square lattice gas with lateral interactions between adparticles. We also have investigated the influence of the attractive and repulsive interactions on both the thermodynamic properties of the lattice gas and the diffusion of adsorbed particles over surface. We have calculated adsorption isotherms and coverage dependences of the pair correlation function, isothermal susceptibility and the chemical diffusion coefficient. In addition, we have included in our analysis the interaction of the activated particle in the saddle point with its nearest neighbors. We have also used Monte Carlo (MC) technique to calculate these dependences. Despite the fact that both methods constitute very different approaches, the correspondence of the numerical data is surprisingly good. Therefore, we conclude that the RSRG approach can be applied to characterize the thermodynamic and kinetic properties of systems of particles with strong lateral interactions. Received 1st September 1998 and Received in final form 8 March 2000     

Electron charge ordering in the extended Hubbard model

The Hubbard model on 3-dimensionalsc lattice with an attractive or repulsive on site interaction, augmented by a renulsive nearest neighbour interaction and its atomic limit are studied using the method of infrared bounds. Conditions upon interactions for the existence of a temperature driven phase transition to so called charge ordered phase are derived. A lower bound in terms of interactions for the corresponding critical temperature is calculated.     

Phase Diagram of 2 × 2 Adsorbates at Surfaces with Hexagonal Symmetry

The phase diagram of a lattice-gas model for 2 2 2 adsorbates at surfaces with hexagonal symmetry has been investigated by Monte Carlo simulations. The model relies on repulsive interactions between the particles for distances up to second nearest neighbor sites. It is shown that first- or second-order phase transitions take place depending on the strength of the interactions. Strong first- or second-neighbor interactions are responsible for a first-order transition while for intermediate interaction strength a second-order transition is possible. The critical exponent for the susceptibility shows the expected value of the four-states Potts model in case of a second-order transition. The value of the critical exponent is reduced when the transition changes from first to second order.     

Symmetry constraints on phonon dispersion in graphene

We calculate the phonon dispersion for graphene with interactions between the first, second, and third nearest neighbors in the framework of the Born-von Karman model taking into account the constraints imposed by the lattice symmetry. Analytical expressions give the nonzero sound velocity for the out-of-plane (bending) mode. The dispersion of four in-plane modes is determined by coupled equations. Values of the force constants are found in fitting with frequencies at critical points and elastic constants measured on graphite.     

Self-organized Criticality in an Earthquake Model on Random Network

A simplified Olami-Feder-Christensen model on a random network has been studied. We propose a new toppling rule — when there is an unstable site toppling, the energy of the site is redistributed to its nearest neighbors randomly not averagely. The simulation results indicate that the model displays self-organized criticality when the system is conservative, and the avalanche size probability distribution of the system obeys finite size scaling. When the system is nonconservative, the model does not display scaling behavior. Simulation results of our model with different nearest neighbors q is also compared, which indicates that the spatial topology does not alter the critical behavior of the system.     

A study of the critical properties of the Ising model on body-centered cubic lattice taking into account the interaction of next behind nearest neighbors

The replica Monte Carlo method has been used to investigate the critical behavior of a threedimensional antiferromagnetic Ising model on a body-centered cubic lattice, taking into account interactions of the adjacent behind neighbors. Investigations are carried out for the ratios of the values of exchange interactions behind the nearest and next nearest neighbors k = J ₂/J ₁ in the range of k ∈ [0.0, 1.0] with the step Δk = 0.1. In the framework of the theory of finite-dimensional scaling the static critical indices of heat capacity α, susceptibility γ, of the order parameter β, correlation radius ν, and also the Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is kept in the interval of k ∈ [0.0, 0.6]. It is established that a nonuniversal critical behavior is observed in the range k ∈ [0.8, 1.0].     

Influence of field on frustrations in low-dimensional magnets

On the base of exact analytical solutions for maximum eigenvalue of Kramers–Wannier transfer matrix the phenomena of frustrations appearance and suppression of phase transition or, on the contrary, the phase transition appearance and suppression of frustrations are studied on the base of exact analytical solutions for 1D Ising model, 3-state, and 4-state standard Potts models with allowance for the interactions between nearest J and next-nearest neighbors J′, for 6-state and 8-state modified Potts models with allowance for the interaction between only nearest neighbors J. In all the models investigated we obtained exact numbers and values of frustrating fields depending, in particular, on mutual orientation of the field and spin directions.     

Frustrations in low-dimensional magnetic systems

On the basis of exact analytical solutions for spin-spin correlation functions in the one-dimensional 3-state [1] and 4-state [2] standard Potts models and Ising model [3] with allowance for the interactions between nearest neighbors J and next-nearest neighbors J′, phenomena of the appearance and disappearance of frustrations have been investigated, depending on the signs of J and J′ and the ratio of the interactions. In the Ising model, these phenomena have been studied on triangular, hexagonal, and kagomé lattices on the basis of exact analytical solutions for the maximum values of the Kramers-Wannier matrices obtained in [4, 5].     

Multiple-quantum dynamics of one-dimensional nuclear spin systems in solids

Multiple-quantum spin dynamics is studied using analytic and numerical methods for one-dimensional finite linear chains and rings of nuclear spins 1/2 coupled by dipole-dipole interactions. An approximation of dipole-dipole interaction between nearest neighbors having the same constants is used to obtain exact expressions for the intensities of the multiple-quantum coherences in the spin systems studied, which are initially in thermal equilibrium and whose evolution is described by a two-spin two-quantum Hamiltonian. An approximation of nearest neighbors with arbitrary dipole-dipole interaction constants is used to establish a simple relationship between the multiple-quantum dynamics and the dynamics of spin systems with an XY Hamiltonian. Numerical methods are developed to calculate the intensities of multiple-quantum coherences in multiple-quantum NMR spectroscopy. The integral of motion is obtained to expand the matrix of the two-spin two-quantum Hamiltonian into two independent blocks. Using the nearest-neighbor approximation the Hamiltonian is factorized according to different values of the projection operator of the total spin momentum on the direction of the external magnetic field. Results of calculations of the multiple-quantum dynamics in linear chains of seven and eight nuclear spins and a six-spin ring are presented. It is shown that the evolution of the intensities of the lowest-order multiple-quantum coherences in linear chains is accurately described allowing for dipole-dipole interaction of nearest and next-nearest neighbors only. Numerical calculations are used to compare the contributions of nearest and remote spins to the intensities of the multiple-quantum coherences.     

Field-induced transition on a triangular plane in the spin-ice compound Dy2Ti2O7

The origin of the lowest-temperature anomaly reported several years ago using a polycrystalline sample of the spin-ice compound Dy2Ti2O7 has remained unresolved. Here we finally clarify its origin by susceptibility measurements down to 65 mK using single crystals under accurate control of the magnetic fields in two independent directions. We demonstrate that the transition is induced under a subtle field combination that precisely cancels the nearest-neighbor spin interactions acting on the spins on the triangular lattice within the pyrochlore structure. Contrary to the other two field-induced transitions, this transition is driven only by the interactions beyond the nearest neighbors. Our observation thus provides the first qualitative evidence for the essential importance of the dipolar interaction beyond the nearest neighbors in the spin ice.     

Theoretical debye-waller factors for the (100) and (110) surfaces of tungsten

The ratios of the atomic mean square displacements at the (100) and (110) surfaces to those in the bulk have been calculated as a function of temperature for the body-centered cubic crystal tungsten. The calculations have been carried out for a slab-shaped crystal in which the atoms interact through central potentials up to fourth neighbors and through a harmonic angle-bending interaction involving pairs of nearest neighbors. The required averages over the two-dimensional Brillouin zone were obtained using sets of special points which are most efficient in finding such averages. A comparison between the theoretical results and the available experimental data is given.