Dynamical phase transitions in the two-dimensional ANNNI model

We study the phase diagram of the two-dimensional anisotropic next-nearest neighbor Ising (ANNNI) model by comparing the time evolution of two distinct spin configurations submitted to the same thermal noise. We clearly see several dynamical transitions between ferromagnetic, paramagnetic, antiphase, and floating phases. These dynamical transitions seem to occur rather close to the transition lines determined previously in the literature.     

Field-induced spin-flip and spin-flip transitions in PrGa2

A detailed neutron diffraction study of a single crystal of hexagonal PrGa₂ under an applied field is presented. The field is applied along the easy [100] direction of the hexagonal plane. The compound exhibits several field-induced magnetic structures and, in particular, an uncompensated long period commensurate antiphase structure defined by the propagation vector (4/27, 4/27, 0) at zero field and below T_t = 3.5 K. Concerning the intermediate magnetic structures below T_t, two types of magnetic phase transitions are observed: a spin-flip transition where one moment per magnetic cell turns over, and a spin-slip transition from the low field commensurate propagation vector (4/27, 4/27, 0) to another commensurate vector (1/7, 1/7, 0). Between T_t and T_N = 7.2 K, the structure becomes apmlitude-modulated with a propagation vector (0.148, 0.148, 0.023). Important and original magnetic domain effects are also observed due to the high degeneracy of the easy direction of the hexagonal plane in both T<T_t and T_t<T<T_N regions.     

Hamiltonian studies of the two-dimensional axial next-nearest-neighbor ising (ANNNI) model

A one-dimensional quantum Hamiltonian which is equivalent to the twodimensional axial next-nearest-neighbor Ising (ANNNI) model is studied through the derivation and analysis of weak- and strong-coupling perturbation expansions. The phase diagram is constructed and the nature of the phase transitions discussed. In particular, we conclude (i) that there is no Lifshitz point on the ferromagnetic/paramagnetic phase boundary, (ii) there appears to be a Lifshitz point on the antiphase/paramagnetic phase, (iii) above the antiphase Lifshitz point the single transition from paramagnetism to the antiphase is probably continuous and marked by algebraic singularities, (iv) below the antiphase Lifshitz point the transition from paramagnetism to the antiphase is via two transitions, the upper of which is probably of the Kosterlitz/Thouless type, (v) the intermediate phase is presumably incommensurate although the perturbation methods do not directly probe this question.     

Mean-field theory of discommensurations in ANNNI-systems

A method which allows a convenient treatment of domain walls and discommensurations (DCs) in spin lattices is used to determine the structure and the free energy of isolated discommensurations in ANNNI systems as well as their interaction energies,. Considered in detail are DCs in the antiphase structure (<2>-phase). The method makes use of an expansion of the mean field equations about the relevant (in the present case the antiphase-)fixed point. Analytical expressions are presented, exhibiting spatial oscillations of the DC-interaction which are shown to be related to the stable focus characteristics of the antiphase fixed point. As a consequence of these oscillations the transitions at the antiphase boundary are of first order everywhere except at themultiphase point.     

Phenomenology of local scale invariance: from conformal invariance to dynamical scaling

Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent θ or a dynamical exponent z. For a given value of θ (or z), we construct local scale transformations, which can be viewed as scale transformations with a space–time-dependent dilatation factor. Two distinct types of local scale transformations are found. The first type may describe strongly anisotropic scaling of static systems with a given value of θ, whereas the second type may describe dynamical scaling with a dynamical exponent z. Local scale transformations act as a dynamical symmetry group of certain non-local free-field theories. Known special cases of local scale invariance are conformal invariance for θ=1 and Schrödinger invariance for θ=2.The hypothesis of local scale invariance implies that two-point functions of quasiprimary operators satisfy certain linear fractional differential equations, which are constructed from commuting fractional derivatives. The explicit solution of these yields exact expressions for two-point correlators at equilibrium and for two-point response functions out of equilibrium. A particularly simple and general form is found for the two-time autoresponse function. These predictions are explicitly confirmed at the uniaxial Lifshitz points in the ANNNI and ANNNS models and in the aging behaviour of simple ferromagnets such as the kinetic Glauber–Ising model and the kinetic spherical model with a non-conserved order parameter undergoing either phase-ordering kinetics or non-equilibrium critical dynamics.     

Transient dynamical behavior and phase transitions in magnetic systems

It was recently suggested that transient dynamical properties were of some use to predict equilibrium critical properties of 2D and 3D models of statistical mechanics on the lattice. We investigate such dynamical properties for three related models with competitive interactions, namely the ANNNI model, the brickwork model, and the BNNNI model. In spite of known differences in their equilibrium phase diagrams, our simulations display similar transient dynamical behaviors for all three models. The reliability of this method for probing equilibrium properties seems therefore questionable even for rather simple magnetic models without any structural disorder.On leave from Centre de Physique Théorique, Ecole Polytechnique, 91128, Palaiseau Cedex, France.     

Rectangular lattice gas model with competing interactions and the two-dimensional ANNNI model in a field

A lattice gas model with short range competing interactions for adsorption on (110) surfaces of fcc crystals, in particular for O/Pd(110), as well as its Ising analog, the two-dimensional ANNNI model with antiferromagnetic axial nearest and next-nearest neighbour interactions in a field, are studied using the free fermion approximation and Monte Carlo techniques. The phase diagrams display different commensurate phases and incommensurate regions. Static and dynamic aspects of topological defects (walls and dislocations) characterising the incommensurate structures are investigated.     

Ising model with frustration,elasticity, and competing interactions

The Ising model on a compressible triangular lattice with axial next-nearestneighbor interactions is studied in the mean-field approximation. A representative phase diagram is generated, which exhibits first- and second-order phase transitions to commensurate modulated phases. The crossover point from first to second order transitions is calculated. The stability of the modulated phases is calculated analytically in a low-temperature approximation. These results are very different from the ANNNI model, which exhibits a second-order transition to a continuum of commensurate and incommensurate phases.     

Damage spreading in 2-dimensional isotropic and anisotropic Bak-Sneppen models

We implement the damage spreading technique on 2-dimensional isotropic and anisotropic Bak-Sneppen models. Our extensive numerical simulations show that there exists a power-law sensitivity to the initial conditions at the statistically stationary state (self-organized critical state). Corresponding growth exponent α for the Hamming distance and the dynamical exponent z are calculated. These values allow us to observe a clear data collapse of the finite size scaling for both versions of the Bak-Sneppen model. Moreover, it is shown that the growth exponent of the distance in the isotropic and anisotropic Bak-Sneppen models is strongly affected by the choice of the transient time.     

Incommensurate structure in the lattice-gas ANNNI model

The phase diagram of the two-dimensional lattice-gas ANNNI model is investigated using the cluster transfer-matrix method. The numerical calculations have shown commensurate, disordered, and floating incommensurate phases. The properties of the incommensurate phase are studied in detail and the position of the Lifshitz point is discussed.     

Relaxation Times in the ASEP Model Using a DMRG Method

We compute the largest relaxation times for the totally asymmetric exclusion process (TASEP) with open boundary conditions with a DMRG method. This allows us to reach much larger system sizes than in previous numerical studies. We are then able to show that the phenomenological theory of the domain wall indeed predicts correctly the largest relaxation time for large systems. Besides, we can obtain results even when the domain wall approach breaks down, and show that the KPZ dynamical exponent z=3/2 is recovered in the whole maximal current phase.     

Continuous quantum phase transitions in the one-dimensional spin-1/2 axial next-nearest-neighbour Ising model in two orthogonal magnetic fields

We have investigated the one-dimensional spin-1/2 axial next-nearest-neighbour Ising (ANNNI) model in two orthogonal magnetic fields at zero temperature. There are four different possible ground state configurations for the ANNNI model in a longitudinal field, in the thermodynamic limit. The inclusion of a transverse field introduces quantum fluctuations which destroy the existing spin order along certain critical lines. The effects of the fluctuations in three of the four ordered regions were investigated using the finite-size scaling technique. The phase boundaries of the ANNNI model in two orthogonal magnetic fields were thus determined numerically. For certain limits of the Hamiltonian we compared the obtained results with the existing literature and our results were in good agreement with the results in the existing literature.     

Ag在Si(111)表面二维生长有序化动力学研究

利用自制的高分辨率衍射斑角分布测量仪对低能电子衍射斑进行测量,研究Ag在Si(111)表面的有序化规律.结果表明,Ag3^1/2畴在生长过程中,满足标度不变性,是一种自相似的生长过程,在生长初期,它的生长指数近似为1/2,并提出了Ag从Ag(111)岛向外扩散形成Ag3^1/2畴的生长机制.还提出利用光助退火以在较低温度下获得完善的表面结构.     

A real-time investigation by RHEED of the homoepitaxial growth of GaAs on (0 0 1) oriented surfaces

In this letter we report on the formation of long-range surface disorder features during the growth by molecular beam epitaxy (MBE) of homoepitaxial GaAs (0 0 1) films having the β2(2 × 4) reconstruction. Observations were made in real-time at the growth temperature using reflection high energy electron diffraction (RHEED) and analyzed kinematically. We show that kinks (cooperative shifts of whole columns of 2 × 4 units along the [1 1 0] direction) form rapidly as growth commences and that the antiphase domain structure present on the substrate prior to growth as a result of the arrangement of As-As dimers persists. This produces a surface with two types of long-range disorder. We speculate on the role of incident Ga atoms on this process.     

Finite-size scaling properties of the damage distance and dynamical critical exponent for the Ising model

With the damage spreading method, scaling properties of the damage distance on the Ising model with heat bath dynamics are studied numerically. With the parallel flipping scheme, the scaling curves fall on two curves, which depend on the odd or even lattice sizes. The both scaling curves give the consistent dynamical exponent as z = 2.16±0.04 for d = 2 and z = 2.09±0.05 for d = 3, respectively. By shifting one of them, two curves overlap each other perfectly. Meanwhile, all the scaling curves obtained by single-spin flipping processes (with different odd or even lattice sizes) fall on a single curve, from which the consistent dynamical critical exponent with the parallel scheme is obtained z = 2.18±0.02 for d = 2 and z = 2.08±0.04 for d = 3.     

Herd formation and information transmission in a population: non-universal behaviour

We present generalized dynamical models describing the sharing of information, and the corresponding herd behavior, in a population based on the recent model proposed by Eguıluz and Zimmermann (EZ) [Phys. Rev. Lett. 85, 5659 (2000)]. The EZ model, which is a dynamical version of the herd formation model of Cont and Bouchaud (CB), gives a reasonable model for the formation of clusters of agents and for actions taken by clusters of agents. Both the EZ and CB models give a cluster size distribution characterized by a power law with an exponent -5/2. By introducing a size-dependent probability for dissociation of a cluster of agents, we show that the exponent characterizing the cluster size distribution becomes model-dependent and non-universal, with an exponential cutoff for large cluster sizes. The actions taken by the clusters of agents generate the price returns, the distribution of which is also characterized by a model-dependent exponent. When a size-dependent transaction rate is introduced instead of a size-dependent dissociation rate, it is found that the distribution of price returns is characterized by a model-dependent exponent while the exponent for the cluster-size distribution remains unchanged. The resulting systems provide simplified models of a financial market and yield power law behaviour with an easily tunable exponent. Received 31 December 2001     

The one-dimensional ANNNI model in a transverse field: analytic and numerical study of effective Hamiltonians

We consider a quantum spin-1/2 Ising chain with competing nearest and next-nearest neighbor interactions in a transverse magnetic field, which is known to be equivalent to the classical two-dimensional ANNNI model. Within a perturbation theory for small transverse field (corresponding to low temperatures in the classical ANNNI model) we derive two effective Hamiltonians: the free model describing free fermions on a fictitious lattice that excludes particular heavy excitations of the original system; and the complete model, which incorporates creation and annihilation of these fermions. Whereas the former possesses only three phases (ferromagnetic, floating and anti phase), the latter contains the full physics of the 2d ANNNI model, including a paramagnetic phase between the ferromagnetic and floating phase and a Kosterlitz-Thouless transition. New analytic results are derived for the free model, e.g. the excitation spectrum that turns out to be non-trivial. Our effective Hamiltonians are defined on a restricted Hilbert space so that exact diagonalization calculations can be done for much larger system sizes. Results from extensive Lanczos calculations for system sizes up to L = 32 are presented confirming the original predictions from Villain and Bak.     

Non-resonant and resonant x-ray scattering studies on multiferroic TbMn2O5

Comprehensive x-ray scattering studies, including resonant scattering at Mn L, Tb L, and M edges, were performed on single crystals of TbMn2O5 for crystallographic data to elucidate the nature of its commensurate and incommensurate phases. The scattering results provide direct evidence of symmetry lowering to the ferroelectric phase driven by magnetically induced lattice modulations and show the presence of multiple magnetic orders. The competing orders under spin-frustrated geometry are believed to cause discommensuration and result in the commensurate-to-incommensurate phase transition around 24 K. It is proposed that the low temperature incommensurate phase consists of commensurate domains separated by antiphase domain walls which change both signs of spontaneous polarizations and x-ray scattering amplitudes for forbidden reflections.     

电压型双频率控制开关变换器的动力学建模与多周期行为分析

在断续导电模式下, 建立了电压型双频率控制开关变换器的动力学模型, 并推导了相应的特征值方程. 根据动力学模型, 采用分岔图研究了电路参数变化时变换器存在的边界碰撞分岔行为和周期2, 周期3,周期4等多周期行为, 结果表明: 变换器经历了周期1态、多周期态、周期1态的分岔路由; 周期态的转变均是由边界碰撞分岔引起的. 根据特征值方程, 采用Lyapunov指数研究了变换器的稳定性, 结果表明: 随着电路参数的变化, Lyapunov指数始终小于零, 变换器一直工作于稳定的周期态, 验证了电压型双频率控制开关变换器的周期3行为并不意味着变换器会必然发生混沌. 通过电路仿真, 分析了负载变化时变换器的时域波形、相轨图和频谱图, 验证了动力学模型的可行性和理论分析的正确性. 实验结果验证了文中的仿真结果. 关键词： 开关变换器 双频率控制 边界碰撞分岔 多周期行为     

The ANNNI model — Theoretical analysis and experimental application

The state of the art on the analysis of axial next-nearest neighbour Ising (or ANNNI) models in one, two, and three dimensions is reviewed. Configurational entropy is shown to play the decisive role in forming spatially modulated spin patterns in this prototype model with discrete symmetry and short-range competing interactions. Among the most prominent features of the model are sequences of distinct, commensurate phases, structure combination branching processes and (floating) incommensurate structures. The results are compared with experimental findings on a variety of systems including alloys, adsorbates, ferroelectrics, magnetic systems, and polytypes.