Application of the renormalization group method to the s = 12XY model on the triangular lattice

The two-dimensional spin one half XY model may undergo an unusual type of phase transition. A formulation of the renormalization group approach of Niemeijer and van Leeuwen suitable for quantum-mechanical systems is presented. The method is applied to the spin one half XY model on the triangular lattice using a second order cumulant expansion based on division of the triangular lattice into seven spin cells. The resulting free energy curve is in excellent agreement with that obtained from the high temperature series expansion. An unstable fixed point is found but the corresponding critical temperature is not in good agreement with the series expansion value. Pathological values are found for the critical exponents.     

Investigation of the Potts Model on Triangular Lattices by the Second Renormalization of Tensor Network States

We employ the second renormalization group method of tensor-network states to investigate thermodynamic properties of the ferromagnetic and antiferromagnetic Potts model on triangular lattices. From the temperature dependence of the internal energy and the specific heat, both the critical temperatures and critical exponents are evaluated. For the q = 3 antiferromagnetic Potts model, the critical temperature is found to be Tc = 0.627163±0.000003, which is at least one order of magnitude more accurate than that obtained by other methods.     

Geometry effect on the magnetic ordering of geometrically frustrated rectangular and triangular magnets

We investigate the effect of geometry on the ground-state ordering of artificially frustrated magnetic rectangular and triangular lattices by Monte Carlo method. By varying the vertical lattice spacing while keeping the horizontal one fixed, we show that when the ratio of vertical to horizontal lattice spacing, labeled by η, is less than 1.82, the ground state of the rectangular lattice presents long-range antiferromagnetic order and for η?1.82 the ground state changes to long-range mixed ferromagnetic and antiferromagnetic order. For the frustrated triangular lattice, the short-range ordered state as well as two long-range ordered ground states occurs transiently at η=0.87 and 2, where the energies of the two ground states with long-range order are approximately equal. In addition, the level of frustration of both frustrated lattices is found to be largely relevant to the ratio η.     

Breakdown of universality in directed spiral percolation

Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated in this model are generally rarefied and have chiral dangling ends on both the square and triangular lattices. It is found that the clusters are more compact and less anisotropic on the triangular lattice than on the square lattice. The elongation of the clusters is in a different direction than the imposed directional constraint on both the lattices. The values of some of the critical exponents and fractal dimension are found considerably different on the two lattices. The DSP model then exhibits a breakdown of universality in 2D between the square and triangular lattices. The values of the critical exponents obtained for the triangular lattice are not only different from that of the square lattice but also different form other percolation models.Received: 12 March 2004, Published online: 23 July 2004PACS: 02.50.-r Probability theory, stochastic processes, and statistics - 64.60.-i General studies of phase transitions - 72.80.Tm Composite materials     

A VARIATIONAL METHOD IN LATTICE GAUGE THEORY BASED ON HÖLDER INTEGRAL INEQUALITY

A variational method based on Hölder integral inequality is presented. Taking the parameters in integral inequality as variational parameters, we can calculate the free energy in lattice gauge system. The plaquatte energy of Z₂ 、U(1)、 SU(2) gauge system is found and consistent with that given by Monte Carlo method. But, the higher phase transitions for U(1), SU(2) gauge systems are not found.     

Theoretical Study of Elastic Properties of Tungsten Disilicide

The plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to analyse the lattice parameters, elastic constants, bulk moduli, shear moduli and Young's moduli of WSi₂. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties and vibrational effects. The athermal elastic constants of WSi₂ are calculated as a function of pressure up to 35GPa. The relationship between bulk modulus and temperature up to 1200K is also obtained. Moreover, the Debye temperature is determined from the non-equilibrium Gibbs function. The calculated results are in good agreement with the experimental data.     

Al70Co15Tb5Ni10合金中准晶相关相的高压研究

 使用静高压熔态淬火方法，在Al₇₀Co₁₅Tb₅Ni₁₀合金中截获到迄今为止晶胞参数最大的两个十次准晶的Penrose-Tiling相关相。其晶胞参数分别为：简单正交晶体a=6.11 nm，b=0.4 nm，c=8.4 nm；底心正交晶体a=6.11 nm，b=0.4 nm，c=8.4 nm。其晶体结构和晶胞参数与目前理论上的预言基本吻合。     

Corrected MK Transformation of ZN Gauge Theory

The corrected Migdal-Kadanoff recurrence relations of lattice gauge systems is obtained and the phase diagram of Z₄ system is calculated.It is found that the fixed poind and the phase diagram obtained in this paper are numerically closer to that given by Monte Carlo simulation.Therefore,the corrected recurrence relation is more significant than MK relation.     

First-Principles Calculations of Elastic Properties of LaNi5 Compound

The equilibrium lattice constants, temperature dependence of bulk modulus, the pressure dependence of the normalized volume V/V0, elastic constants Cij and bulk modulus of LaNi5 crystal are obtained using the firstprincipies piane-wave pseudopotential method in the GGA-PBE generalized gradient approximation as well as the quasi-harmonic Debye model. We analyse the relationship between bulk modulus and temperature up to 2000 K and obtain the relationship between bulk modulus B and pressure at diFFerent temperatures. It is found that the bulk modulus B increases monotonously with increasing pressure. Moreover, the pressure dependences of Debye temperatures and the pressure derivatives of lattice constants are also successfully obtained. The calculated results are in agreement with the experimental data and the other theoretical results.     

Analytical Study of Lattice U(1) Gauge-Higgs ModelsWith Fixed Modulus

Using variational cumnulant expansion we study the lattice U(1) gauge-Higgs models with fixed modulus To determine the variational parameters, we combine main-value method and accumulated point method. The phase diagrams obtained are consistent with Monte Carlo results. We also calculate Polyakov line 〈L〉 with N_τ=1 in finite temperature.     

高压截获十次准晶相关晶体相和纳米级超微粒

 对Al₇₀Co₁₅Ni₁₀Tb₅合金进行了静高压（7.0 GPa）熔态（1 700 ℃）淬火（冷却速率10²⁰ C/s）处理，首次观察到一个新十次准晶相关晶体相。该相属底心正交晶体，晶胞参数为a=2.28 nm、b＝1.60 nm、c＝5.46 nm。通过高分辨像分析，给出了它的二维点阵模型。同时在样品中发现了尺寸均匀的纳米级非晶超微粒形成，超微粒为球形，直径30~40 nm。     

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.     

高压下SiO_2的第一性原理计算

基于密度泛函理论(DFT)的第一性原理,采用Hartree-Fork(HF)方法,分别计算了Si O2的α-石英结构、金红石结构以及氯化钙结构的总能量随体积的变化关系。利用Murnaghan状态方程,通过能量和体积拟合,得到了3种结构的体变模量及其对压强的一阶导数。计算结果表明,随着压强的增加,Si O2会从α-石英结构转变为金红石结构,与实验结果和其它理论结果一致;金红石结构与氯化钙结构之间不存在相变,可以共存。此外,对具有α-石英结构的Si O2的晶格常数、电子态密度和带隙随压强的变化关系进行了计算和分析,结果表明:加压作用下,能带向高能方向移动,Si─O键缩短,电子数转移增加,带隙展宽,电荷发生重新分布。     

First-Principles Calculations of Elastic and Thermal Properties of Molybdenum Disilicide

The first-principles plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to anaylse the equilibrium lattice parameters, six independent elastic constants, bulk moduli, thermal expansions and heat capacities of MoSi2. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties, thermodynamic properties and vibrational effects. The calculated zero pressure elastic constants are in overall good agreement with the experimental data. The calculated heat capacities and the thermal expansions agree well with the observed values under ambient conditions and those calculated by others. The results show that the temperature has hardly any effect under high pressure.     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

THE WILSON LOOP EXPECTATION VALUES IN 2-AND 3-DIMENSIONAL su(2) LGT

An improved Monte Carlo scheme is applied to the computation of the expectation values of nxm Wilson loops in both 2-and 3-dimensional SU(2) lattice gauge theories.The results are compared with those simulated by the discrete group Y₁₂₀ and the exact results in two dimensions.     

The bond bending model on triangular lattice and square lattice

The bond bending model is studied using the series expansion method on a triangular lattice and on a square lattice. The elastic splay susceptibility χ_SR and the elastic compressional susceptibility χ_el are calculated up to 11th order for the triangular lattice and up to 14th order for the square lattice. The elastic splay crossover exponent, ζ_SP, is found to be ζ_SP ≈ 1.26 ± 0.05 for the triangular lattice and ζ_SP = 1.30 ± 0.04 for the square lattice which is close to the conductivity exponent, ζ_Re, of the resistor network. From the scaling relation ? _B = dv + ζ_SP, we found that the bulk modulus exponent ? _B = 3.93 ± 0.05 for the triangular lattice and ? _B = 3.97 ± 0.04 for the square lattice which is in good agreement with the result ? _B = 3.96 ± 0.04, obtained by Zabolitzky et al. using a transfer matrix technique on a honeycomb lattice.     

Diffusion in Lorentz lattice gas cellular automata: The honeycomb and quasi-lattices compared with the square and triangular lattices

We study numerically the nature of the diffusion process on a honeycomb and a quasi-lattice, where a point particle, moving along the bonds of the lattice, scatters from randomly placed scatterers on the lattice sites according to strictly deterministic rules. For the honeycomb lattice fully occupied by fixed rotators two (symmetric) isolated critical points appear to be present, with the same hyperscaling relation as for the square and the triangular lattices. No such points appear to exist for the quasi-lattice. A comprehensive comparison is made with the behavior on the previously studied square and triangular lattices. A great variety of diffusive behavior is found, ranging from propagation, superdiffusion, normal, quasi-normal, and anomalous, to absence of diffusion. The influence of the scattering rules as well as of the lattice structure on the diffusive behavior of a point particle moving on the all lattices studied so far is summarized.     

Majority rule at low temperatures on the square and triangular lattices

We consider the majority-rule renormalization group transformation applied to nearest neighbor Ising models. For the square lattice with 2 by 2 blocks we prove that if the temperature is sufficiently low, then the transformation is not defined. We use the methods of van Enter. Fewrnández, and Sokal, who proved the renormalized measure is not Gibbsian for 7 by 7 blocks if the temperature is too low. For the triangular lattice we prove that a zero-temperature majorityrule transformation may be defined. The resulting renormalized Hamiltonian is local with 14 different types of interactions.     

Photonic band gaps in two-dimensional photonic crystals of core-shell-type dielectric nanorod heterostructures

A new type of two-dimensional photonic crystal (PC) called core-shell-type PC composed of a nanorod heterostructure array in a square or triangular lattice such that a dielectric nanorod is covered by a thin interfacial layer is studied. Using the plane-wave numerical expansion method, we study the modification of the band gap spectrum when the nanorods are covered by other material, and reveal that the photonic band gap is considerably enhanced in size for both square and triangular lattice. The effects of structural parameters on the band gaps are also studied. The results show that there exist optimal parameters to open large gaps, and TE (Transverse-electric) band gaps are favored in a triangular lattice.