二维棋盘格子复式晶格的完全光子带隙研究

设计了一种棋盘格子复式晶格的二维光子晶体：在二维正方形格子中，把截面为正方形的柱子旋转45°，同时在每个原胞中心引入一个圆形截面的柱子构成的光子晶体结构. 用平面波展开计算棋盘格子复式晶格的完全光子带隙，结果表明：棋盘格子复式晶格的完全光子带隙的Δω/ω比值几乎是普通棋盘格子的5倍，完全光子带隙的个数也增加. 与其他复式结构相比较，发现其最佳的Δω/ω比值是一类粗锐复合结构光子晶体的2.1倍. 关键词： 二维光子晶体 复式晶格 完全光子带隙     

Exact variational methods and cluster-variation approximations

It is shown that for classical,d-dimensional lattice models with finite-range interactions the translation-invariant equilibrium states have the property that their mean entropy is completely determined by their restriction to a subset of the lattice that is infinite in (d–1) dimensions and has a width equal to the range of the interaction in the dth dimension. This property is used to show proper convergence toward the exact result for a hierarchy of approximations of the cluster-variation method that uses one-dimensionally increasing basis clusters in a two-dimensional lattice.     

Internal space decimation for lattice gauge theories

By a systematic decimation of internal space lattice gauge theories with continuous symmetry groups are mapped into effective lattice gauge theories with finite symmetry groups. The decimation of internal space makes a larger lattice tractable with the same computational resources. In this sense the method is an alternative to Wilson's and Symanzik's programs of improved actions. As an illustrative test of the method U(1) is decimated to Z(N) and the results compared with Monte Carlo data for Z(4)- and Z(5)-invariant lattice gauge theories. The result of decimating SU(3) to its 1080-element crystal-group-like subgroup is given and discussed.     

Hadron interactions in lattice QCD

Progress on the potential method, recently proposed to investigate hadron interactions in lattice QCD, is reviewed. The strategy to extract the potential in lattice QCD is explained in detail. The method is applied to extract NN potentials, hyperon potentials and the meson–baryon potentials. A theoretical investigation is made to understand the origin of the repulsive core using the operator product expansion. Some recent extensions of the method are also discussed.     

Poisson Approximations for the Ising Model

A d-dimensional Ising model on a lattice torus is considered. As the size n of the lattice tends to infinity, a Poisson approximation is given for the distribution of the number of copies in the lattice of any given local configuration, provided the magnetic field a = a(n) tends to −∞ and the pair potential b remains fixed. Using the Stein-Chen method, a bound is given for the total variation error in the ferromagnetic case. AMS SUBJECT CLASSIFICATION: 60F05, 82B20.     

Quantum spin liquid on 2D rectangular frustrated AF lattice

The state of a 2D rectangular spin lattice with first, second and third nearest-neighbour anisotropic antiferromagnetic interactions is investigated. In a special line of parameter space, it is proved that the quantum spin liquid is the exact eigenstate of the system. For general parameter values, Green's function method with cut-off approximation is used to determine the phase diagram at zero temperature, and it is found that the quantum spin liquid appears on a rectangular lattice when the third nearest-neighbour interaction in the direction with shorter lattice spacing is introduced. The relations to the possibility of mixture of the spin liquid and the Fermi liquid in high-T _c superconductors are discussed.     

Duality in two-dimensional Z(N)-symmetric spin models on a finite lattice

We propose a method for deriving duality relations for two-dimensional inhomogeneous Z(N)-symmetric models on a finite square lattice wound around a torus. The method is used to obtain duality relations for the vector Potts model, the Berezinskii-Villain Z(N)-model, the Ashkin-Teller model, and the 8-vertex model on a lattice obliquely wound around a torus, as well as an exact relation linking the partition functions of the latter two models. Zh. éksp. Teor. Fiz. 113, 240–260 (January 1998)     

Efficient Implementation of the Pivot Algorithm for Self-avoiding Walks

The pivot algorithm for self-avoiding walks has been implemented in a manner which is dramatically faster than previous implementations, enabling extremely long walks to be efficiently simulated. We explicitly describe the data structures and algorithms used, and provide a heuristic argument that the mean time per attempted pivot for N-step self-avoiding walks is O(1) for the square and simple cubic lattices. Numerical experiments conducted for self-avoiding walks with up to 268 million steps are consistent with o(log N) behavior for the square lattice and O(log N) behavior for the simple cubic lattice. Our method can be adapted to other models of polymers with short-range interactions, on the lattice or in the continuum, and hence promises to be widely useful.     

Perturbation theory for calculating solitary waves in one-dimensional lattices

A systematic method is given to compute solitary waves in one-dimensional lattices. The procedure, based on perturbation theory, leads to an infinite series, which has to be summed up completely. This can be done by the use of Padé approximation or a pseudo-potential method. We obtain exact results in the case of the Toda lattice and good approximations for solitary waves in non-integrable systems. For the Toda lattice also theN-soliton solution is calculated.     

Game of Life on the Equal Degree Random Lattice

An effective matrix method is performed to build the equal degree random (EDR) lattice, and then a cellular automaton game of life on the EDR lattice is studied by Monte Carlo (MC) simulation. The standard mean field approximation (MFA) is applied, and then the density of live cells is given ρ=0.37017 by MFA, which is consistent with the result ρ=0.37±0.003 by MC simulation.     

A note on mean-field behavior for self-avoiding walk on branching planes

We consider the critical behavior of the susceptibility of the self-avoiding walk on the graphT×Z, whereT is a Bethe lattice with degreek andZ is the one dimensional lattice. By directly estimating the two-point function using a method of Grimmett and Newman, we show that the bubble condition is satisfied whenk>2, and therefore the critical exponent associated with the susceptibility equals 1.     

Optical absorption of the F center as function of the temperature

Abstract

The temperature shift of the F absorption band for KBr and KCl single crystals was experimentally and theoretically determined. The theoretical calculations are based on the pseudopotential method using different wave functions and assumed a linear thermal expansion coefficient for the crystalline lattice. The change of F-center absorption energy due to collisions with the thermally vibrating lattice is calculated. This contribution is small. The measurements agree fairly well with the results obtained using the present model.     

Determining orientation relationships for the <Emphasis Type="Italic">B</Emphasis>2 → <Emphasis Type="Italic">B</Emphasis>19′ transformation in single crystal titanium nickelide according to the texture of <Emphasis Type="Italic">B</Emphasis>19′ martensite

A precision method for determining orientation relationships upon the B2 → B19′ transformation in titanium nickelide has been developed. The method is based on analyzing the martensite texture formed in the initial high-temperature B2 phase of a single crystal having a high degree of perfection. The orientation relationships between the B19′ lattice and the initial B2 lattice of the TiNi single crystal were established from the B19′ martensite texture formed in single crystals of titanium nickelide upon the B2 → B19′ transformation and from measurements of the lattice parameters. Crystal mechanism of B19′ martensite was proposed which included the shear in the (21-1) B2 plane in the direction [−11-1] B2 by 10°. Such a shear system is typical of the bcc crystals at deformation by twinning. Absolute shear values are in a ratio of 1:4 for B2 → B19′ transformation and for twinning, respectively. Martensite deformation at an invariant lattice is accompanied by small rotations of martensite crystals (±1.6°), that increases the quantity of martensite orientations from 12 to 24.     

Testing two versions of lattice gauge theory: Creutz ratios inU(1)3

In our simplicial version of lattice gauge theory, we approximate Euclidean path integrals by tiling space-time with simplexes and by linearly interpolating the fields throughout each simplex from their values at the vertices. We compare this method with Wilson's lattice gauge theory forU(1) in three dimensions. As a standard of comparison, we compute the exact values of Creutz ratios of Wilson loops in the continuum theory. Monte Carlo computations using the simplicial method give Creutz ratios within a few percent of the exact values for reasonably sized loop atβ=1, 2, and 10. Similar computations using Wilson's method give ratios that typically differ from the exact values by factors of 2 or more for 1⩽β⩽3.5 and that have the wrongβ dependence. The better accuracy of the simplicial method is due to its use of the action and domain of integration of the exact theory, unaltered apart from the granularity of the simplicial lattice. We also present data on the action density and the mass gap. Research supported by the U.S. epartment of Energy under grant DE-FG04-84ER40166.     

Lattice parameter and alloy fraction determination of Pb x Sn1−x Te films by RHEED double-patterns

A new technique to determine simultaneously the structure, the lattice parameter and the alloy stoichiometric composition of Pb _x Sn_1−x Te films r.f. sputtered into different substrates has been developed by making use of Reflection High Energy Electron Diffraction (RHEED) double-patterns. This method is available with all the materials for which the lattice constant is related to the alloy composition.     

Real-space renormalization group for two-dimensional quantum spin systems

A generalization of the Niemeijer and Van Leeuwen real-space renormalization group method for quantum lattice spin systems is presented. A proposed rotationally invariant transformation which preserves the symmetry of the spin space is applied to several quantum systems on a triangular lattice. For the spin-1/2XY-model in both first- and second-order cumulant expansions a nontrivial fixed point exists, giving in the best approximation a critical interactionK _XY ^c =0.453 and critical exponent =1.65. A method of the reduction of the generalized arbitrary spin anisotropic Heisenberg model to the spin-half model is presented.     

Real space renormalization group with effective interactions: applications to 2-D spin lattices

The Blochs theory of effective Hamiltonians has been used to improve the Real Space Renormalization Group approach. The effective interactions between elementary blocks of a periodic lattice can be extracted from the knowledge of the spectrum of the dimers or trimers of blocks. The potentialities of the method are illustrated on a series of quasi 1-D and 2-D problems. The spin gap of two-leg ladders is calculated and an estimate of the impact of ferromagnetic couplings between two-leg ladders on the gap is presented. The method satisfactorily identifies the phase transitions in the 1/5-depleted square lattice as well as in the spin-frustrated Shastry-Sutherland lattice. The J ₂/J ₁ checkerboard lattice is studied and a location of the phase transition between the Néel phase and the dimer phase is proposed.Received: 11 June 2004, Published online: 30 September 2004PACS: 71.10.-W Theories and models of many-electron systems - 71.15.Nc Total energy and cohesive energy calculations - 75.10.-b General theory and models of magnetic ordering     

Casimir Effect on a Finite Lattice

Lattice quantum field theory is a well established branch of modern quantum field theory (QFT). However, it has only peripherally been used for the investigation of Casimir systems — i.e. for systems in which quantum fields are distorted by their interaction with classical background objects. This article presents a Hamiltonian lattice formulation of static Casimir systems at a level of generality appropriate for an introductory investigation. Background structure — represented by a lattice potential V(x) — is introduced along one spatial direction with translation invariance in all other spatial directions. It is simple to extend this formulation to include arbitrary background structure in more than one spatial direction. Following some general analysis two specific finite 1D lattice QFT systems are analyzed in detail. The first has three Dirichlet boundaries at the lattice sites x = 0, l and L (L > l > 0) with vanishing lattice potential V(x) everywhere in between. The vacuum energy and vacuum stress tensor T^μν for this system are calculated in 0 < x < L. Very careful attention must be and is given to renormalization in the (continuum) limit of vanishing lattice constant. Globally and locally this lattice system is seen to closely mimic the corresponding 1D continuum system — as one would hope. Then we introduce a lattice potential V(x) = c/(x — x₀)² centered at x = x₀ < 0 to the left of the boundary at x = 0 and extending through this boundary and the middle Dirichlet boundary at x = l out to the right‐hand boundary x = L > l and beyond. The vacuum energy and T^μν are calculated for this far more complicated system in the region 0 〈 x < L, again with very good results. The internal consistency of the lattice version of this system is carefully examined. Our conclusion is that finite‐lattice formulation provides a powerful and effective tool, capable of solving completely many Casimir systems which could not possibly be handled using continuum methods. This is precisely our reason for introducing it. Future investigations (in one and more dimensions and in dynamical as well as static contexts) will display more fully the power of this method.     

The electronic states in diamond

An account of a method of performing a priori tight-binding calculations on a crystal lattice of the diamond type is given. The method is a generalization of that of Cohan et al. [8]. Certain possible extensions of the method are discussed. New results for the electronic energy bands in diamond are presented in which the variation of the bands with the hybridization parameter of the initial bonding orbitals and the orbital exponent of the basic atomic orbitals is investigated.     

Quantum corrections for lattice gases

Classical lattice gases consisting of structureless particles (with spin) have been quantized by introducing a kinetic energy operator that produces nearest-neighbor hops. Systematic quantum corrections for the partition function and the particle distribution functions appear naturally as power series inX = ²/2ml ² ( ^–1 =k _B T,m is the mass,l is a distance related to lattice spacing). These corrections require knowledge of certain particle displacement probabilities in the corresponding classical lattice gases. Leading-order corrections have been derived in forms that should facilitate their use in computer simulation studies of lattice gases by the standard Monte Carlo method.