Anisotropic Hubbard model on a triangular lattice — spin dynamics in HoMnO3

The recent neutron scattering data for spin-wave dispersion in HoMnO₃ are well-described by an anisotropic Hubbard model on a triangular lattice with a planar (XY) spin anisotropy. Best fit indicates that magnetic excitations in HoMnO₃ correspond to the strong-coupling limit U/t >∼ 15, with planar exchange energy J = 4t ² /U ≃ 2.5 meV and planar anisotropy ΔU ≃ 0.35 meV.      

Microscopic phonon theory of Si/Ge nanocrystals

Microscopic phonon theory of semiconductor nanocrystals (NCs) is reviewed in this paper. Phonon modes of Si and Ge NCs with various sizes of up to 7 nm are investigated by valence force field theory. Phonon modes in spherical SiGe alloy NCs approximately 3.6 nm (containing 1147 atoms) in size have been investigated as a function of the Si concentration. Phonon density-of-states, quantum confinement effects, as well as Raman intensities are discussed.      

Lattice Dynamics at Zone-Center of Sulphide and Selenide Spinels

A rigid-ion model is used to calculate the force constants and effective dynamical charges of sulphide and selenide spinels. The Raman and infrared phonon modes of normal cubic sulphide spinels MCr₂Se₄ (M = Mn, Co, Fe, Hg, Zn, and Cd) and selenide spinels MCr₂Se₄ (M = Hg, Zn, and Cd) are calculated at the first Brillouin zone-centre using above model. The significant outcome of the present work is (i) the interatomic interaction between Cr-S (Se) dominates over the Cr-S(Se) and S-S(Se-Se) type of interatomic interactions, (ii) the effective dynamical charges of the bivalent metal ions are nearly zero, and (iii) the selenide spinels are less ionic than the sulphide spinels and the ionicity decreases as MnCr₂S₄ > FeCr₂S₄ > CoCr₂S₄ > and CdCr₂C₄ > ZnCr₂C₄ > HgCr₂C₄ (C = S and Se). The zone-center phonon frequencies, calculated using these parameters, are found to be in very good agreement with the observed results.     

Lattice dynamical study of body-centred tetragonal indium

The phonon dispersion curves, phonon frequency distribution function as well as the lattice specific heat of body-centred tetragonal indium have been deduced using a lattice dynamical model which includes central, angular and volume forces. Six elastic constants, four zone boundary frequencies and an equilibrium condition were used in the evaluation of the force constants. It is shown that this model is elastically consistent and satisfies the symmetry requirements of the lattice, the phonon frequencies of indium deduced from it are in very good agreement with the experimental values of Reichardt and Smith and the theoretical values of Garrett and Swihart, and theθ _D values compare well with the experimental values over a wide temperature range. The apparent discrepancies in the phonon dispersion curves and theθ _D-T curves obtained from deficient models, importance of umklapp processes and the significance of angular forces in the lattice dynamical models are discussed.     

Tracer diffusion in lattice gases

It has been proved that a tracer particle in a reversible lattice gas converges to Brownian motion. However, only in a few particular cases has a strictly positive self-diffusion coefficientD been established. Here we supply the missing piece and show thatD>0 in general. The exceptions are one-dimensional lattice gases with nearest neighbor jumps only, for whichD=0. The proof establishes a variational formula forD which could be used to obtain realistic bounds.     

激励介质中非线性化学波的格子Boltzmann模型

构造了用于非线性化学波的格子Boltzmann模型.通过设置无对流速度场,使用多重尺度和Chapman Enskog展开,得到了平衡态分布函数的各向同性解.算例考虑了用划痕起搏,在ε²尺度上给出了Selkov系统的模拟结果,再现了远离热力学平衡态的螺旋波结构的经典结果,并与传统数值方法及实验结果进行了比较.     

Infrared asymptotic freedom of a hierarchical φ 3 6 lattice theory

For the weakly coupled lattice ₃ ⁶ theory in a hierarchical model approximation a nonperturbative renormalization group analysis in the spirit of Gawedzki and Kupiainen is performed to study the flow of the effective actions. We deduce a domain of attraction to the tricritical (Gaussian) fixed point. The two relevant coupling constants of the problem are controlled by analytic continuation to complex domains, tracing their images under the renormalization group iterations.     

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733.