Multicanonical sampling of the space of states of ℋ(2, <Emphasis Type="Italic">n</Emphasis>)-vector models

Problems of temperature behavior of specific heat are solved by the entropy simulation method for Ising models on a simple square lattice and a square spin ice (SSI) lattice with nearest neighbor interaction, models of hexagonal lattices with short-range (SR) dipole interaction, as well as with long-range (LR) dipole interaction and free boundary conditions, and models of spin quasilattices with finite interaction radius. It is established that systems of a finite number of Ising spins with LR dipole interaction can have unusual thermodynamic properties characterized by several specific-heat peaks in the absence of an external magnetic field. For a parallel multicanonical sampling method, optimal schemes are found empirically for partitioning the space of states into energy bands for Ising and SSI models, methods of concatenation and renormalization of histograms are discussed, and a flatness criterion of histograms is proposed. It is established that there is no phase transition in a model with nearest neighbor interaction on a hexagonal lattice, while the temperature behavior of specific heat exhibits singularity in the same model, in case of LR interaction. A spin quasilattice is found that exhibits a nonzero value of residual entropy.     

Equilibrium configurations and phase transitions in dipole lattices

Two-dimensional square and hexagonal lattices of magnetic dipoles with the number of rows 1–4 have been studied. Based on the numerical analysis, equilibrium stable domain configurations, including the minimum number of lattice dipoles, have been revealed; the conditions for the creation and destruction of domains have been determined; and their associated changes in the magnetic moment of the lattice and in the energy of the dipole interaction have been found. The conditions for the occurrence of phase transitions that change the configuration of the lattices have been investigated and the conditions for unidirectional propagation of the front of the phase transition have been established. A comparative analysis of different square and hexagonal lattices has been performed in terms of the specific features of the formed domains and the observed orientation phase transitions.     

A LEED-AES study of the oxidation of Fe (110) and Fe (100)

Simultaneous LEED and AES observations have been used to study the initial stages of oxidation of the Fe(110) and Fe(100) single crystal surfaces at 300 K and 400 K and of a clean Fe polycrystal at 300 K. Accurate surface lattice spacings of the precursory oxide structures have been measured and attempts have been made to quantitatively evaluate the corresponding surface oxygen density.On the (110) single crystal surface the final structure is FeO-like with a lattice spacing 4% larger than that of bulk FeO. The transition to the FeO-like structure starts with a surface lattice expansion in the [11&#x0304;0] direction followed by an expansion in the [001] direction in order to accommodate the (111) face of the FeO-like structure. On the (100) single crystal face the oxygen and iron form an fcc (100) face which initially contracts and then expands with increasing oxygen doses. The structure formed at 300 K is spinel-like but heat treatment causes a transition to FeO(100).The changes of the surface unit cell dimensions are interpreted as the result of an interaction between adsorbate and substrate. This interaction is strongest in a direction parallel to the close packed rows of the substrate, making the corresponding periodicity of the adsorbate more resistant to lattice changes.In the case of the polycrystal a hexagonal structure was observed after oxygen adsorption with no simple relation to the oxide structures observed on the single crystals. The initial sticking coefficients in the interval 0–10^?5 torr sec ranged from 0.07 to 0.36 depending on temperature and crystal face observed. The latter dependence is explained in terms of the surface structure.     

Effects of Field Orientation on the Driven Lattice Gas

Steady states of the driven lattice gas (DLG) on triangular, hexagonal and square lattices with the field at several fixed orientations to the principal lattice vectors were studied by Monte Carlo simulation. In most cases a strong field suppressed change to a low-temperature ordered phase. On each lattice, one field orientation that caused nonequilibrium ordering was identified. On triangular and hexagonal lattices, dependence of energy and anisotropy on field strength was studied at those orientations. Anisotropic ordering along the field developed at intermediate temperatures under weak fields. Partial ordering along the field persisted to low temperature under strong fields.     

Superlight small bipolarons in the presence of a strong Coulomb repulsion

We study a lattice bipolaron on a staggered triangular ladder and triangular and hexagonal lattices with both long-range electron-phonon interaction and strong Coulomb repulsion using a novel continuous-time quantum Monte Carlo algorithm to solve the two-particle Coulomb-Fr?hlich model. The algorithm is preceded by an exact integration over phonon degrees of freedom, and as such is extremely efficient. The bipolaron effective mass and radius are computed. Bipolarons on lattices constructed from triangular plaquettes have a novel crablike motion, and are small but very light over a wide range of parameters. We discuss the conditions under which such particles may form a Bose-Einstein condensate with high transition temperature, proposing a route to room temperature superconductivity.     

Periodic overlayers and moiré patterns: theoretical studies of geometric properties

Single crystal surfaces with periodic overlayers, such as graphene on hexagonal metal substrates, are found to exhibit, apart from their intrinsic periodicity, additional long-range order expressed by approximate surface lattices with large lattice constants. This phenomenon can be described as geometrically analogous to lateral interference effects resulting in periodic moiré patterns which are characterized by two-dimensional moiré lattices. Here we discuss in detail the mathematical formalism determining such moiré patterns based on concepts of two-dimensional Fourier transformation including coincidence lattices. The formalism provides simple relations that allow one to calculate possible moiré lattice vectors in their dependence on rotation angles α and scaling factors p1,p2 for periodic (p1 × p2)Rα overlayers on substrate surfaces described by general Bravais lattices. Specific emphasis will be given to hexagonal lattices where experimental data are available.     

Temperature dependence of the electric quadrupole interaction at scandium impurities in zirconium and hafnium

The PAC probe⁴⁴Sc was employed to study the magnitude and temperature dependence of the electric quadrupole interaction at the site of the transition metal Sc in the hexagonal host lattices Zr and Hf. In Zr ∼ 100% of the probe atoms were situated on regular lattice sites and a quadrupole interaction frequency of υ_Q=7.8(1)MHz was measured at room temperature. For Hf the fraction of the probe atoms on regular lattice sites was smaller and a damping of the interaction pattern (υ_Q=9.3(5)MHz at 293 K) could not be excluded. The temperature dependence of the electric field gradient in both host lattices was found to be weak.     

A simple method for fabricating two- and three-dimensional photorefractive photonic lattices microstructures

We demonstrate an approach for easy fabrication of two- and three-dimensional optically induced nonlinear photonic lattices microstructures in photorefractive crystal by applying spatial filter and amplitude mask. The experimental setup of this method is very simple and flexible without complicated optical adjustment system. It can be applied in almost any optical laboratories. Two-dimensional hexagonal, square and three-dimensional hexagonal nonlinear photonic lattices microstructures have been produced in an iron-doped lithium niobate photorefractive crystal. The period of the induced photonic lattices microstructures can be dominated easily. This method is easily extended to generate more complex photonic lattices microstructures in photorefractive crystals, such as quasicrystal lattice.     

Deformation resonance approach to adsorbate induced relaxation

Adsorbate induced modifications of the surface lattice dynamics are of particular interest with respect to surface reconstruction and relaxation. We report on a theoretical attempt of disclosing the microscopic mechanism of an adsorbate driven change of the surface geometry in the early stages of adsorption. The theoretical framework is the deformation resonance approach (DRA), which has been developed for the investigation of inelastic gas - surface interactions. The adsorbate - phonon interaction is of short range and therefore treated in a localized basis set. The local deformation of the surface in the environment of the adsorbed particle is calculated self-consistently using quantum mechanics. Qualitative aspects of the correlated adsorbate - substrate motion are discussed paying special attention to the possibility of adsorbate induced soft phonon modes.The method is applied to studying the interaction of a hydrogen atom with the nickel (110) - surface. The three-dimensional static potential energy surface including the first and second derivatives with respect to the substrate atom displacements has been evaluated using a sophisticated electronic model Hamiltonian. Many - body forces lead to a modification of the coupling between substrate atoms as compared to the clean surface. The metal atoms relax from their original equilibrium positions in order to minimize the total ground state energy of the interacting system. This behaviour is discussed as a possible driving force for the hydrogen induced reconstruction.     

Thermodynamic and magnetic properties in two artificial frustrated lattices

With the Monte Carlo simulation, we investigate the thermodynamics and magnetic properties of the artificial frustrated square and honeycomb lattices. The results from the Ising-like dipolar model show that there occurs one magnetic order transition for the square lattice while the honeycomb lattice exhibits two magnetic order phase transitions. When the magnetic field is applied perpendicular to one of sublattices, a sharp field-independent peak in the specific heat curves appears at a very low temperature for both frustrated lattices due to the occurrence of a long-range ordered state induced by the magnetic field. For the square lattice, the coercive field slightly increases with the angle of field relative to the vertical axis. For both frustrated lattices, the magnetic reversal is achieved mostly via flipping a chain of the nearest neighbor spins.     

Dimer problem on the cylinder and torus

We obtain explicit expressions of the number of close-packed dimers and entropy for three types of lattices (the so-called 8.8.6, 8.8.4, and hexagonal lattices) with cylindrical boundary condition and the entropy of the 8.8.6 lattice with toroidal boundary condition. Our results and the one on 8.8.4 and hexagonal lattices with toroidal boundary condition by Salinas and Nagle [S.R. Salinas, J.F. Nagle, Theory of the phase transition in the layered hydrogen-bonded SnCl²⋅2H₂O crystal, Phys. Rev. B 9 (1974) 4920-4931] and Wu [F.Y. Wu, Dimers on two-dimensional lattices, Inter. J. Modern Phys. B 20 (2006) 5357-5371] imply that the 8.8.6 (or 8.8.4) lattices with cylindrical and toroidal boundary conditions have the same entropy whereas the hexagonal lattices have not. Based on these facts we propose the following problem: under which conditions do the lattices with cylindrical and toroidal boundary conditions have the same entropy?     

Interaction of in-band and in-gap lattice soliton trains in optically induced two-dimensional photonic lattices

We demonstrate the coherent interactions of lattice soliton trains, including in-band solitons (IBSs) and gap soliton trains (GSTs), in optically induced two-dimensional photonic lattices with self-defocusing nonlinearity. It is revealed that the $\pi$-staggered phase structures of the lattice soliton trains will lead to anomalous interactions. Solely by changing their initial separations, the transition between attractive and repulsive interaction forces or reversion of the energy transfer can be obtained. The `negative refraction' effect of the soliton trains on the interaction is also discussed. Moreover, two interacting IBSs can merge into one GST when attraction or energy transfer happens.     

Anomalous interactions of spatial gap solitons in optically induced photonic lattices

We demonstrate coherent interactions between spatial gap solitons in optically induced photonic lattices. Because of the "staggered" phase structures, two in-phase (out-of-phase) bright gap solitons can repel (attract) each other at close proximity, in contrast to soliton interaction in homogeneous media. A reversal of energy transfer direction and a transition between attractive and repulsive interaction forces can be obtained solely by changing the initial soliton separation relative to the lattice spacing.     

用多光束干涉模拟晶格图案

利用多束激光干涉，可形成三维晶格结构，计算结果指出，用四束光或六束光可形成大部分的布拉格（Ｂｒａｇｇ）点阵。同时用Ｈｅ－Ｎｅ激光器获得了体心正方和面心立方的相干图案，晶格常数和计算结果相符，该研究对构成可见和红外区域的光子晶有一定意义。     

Magnetic properties of 2D nano-islands I: Ising spin model

An Ising spin effective field theory (EFT) is developed as a framework for a detailed analysis of the magnetic properties of two-dimensional (2D) nano-islands on a nonmagnetic substrate with an out of plane magnetization. The Hamiltonian with nearest neighbor exchange interactions and single-atom magnetic anisotropy defines the ground state. The calculation yields the single site spin correlations, the magnetizations, and the isothermal susceptibilities for the core and periphery domains, and the island core phase diagrams. The choice of a spin S=1 for the atoms permits the analysis of the effects of spin fluctuations via the single site spin correlations. In particular we investigate the effects due to the different anisotropies and reduced dimensionalities for the core and periphery domains. The present model calculations are developed for different 2D nano-islands lattices. Detailed theoretical results are presented for the square and hexagonal lattices, with numerical applications for the 2D Co nano-islands on Pt. The derived transition temperature for the hexagonal lattice nano-islands is in good agreement with the experimental data for Co nano-islands on Pt. Though both the core and the periphery domains have the same order-disorder transition temperature, the magnetization of each domain attains this transition differently. The temperature behavior of the spin correlations is also fundamentally different for the periphery and core sites, which entails distinctly different isothermal susceptibilities, and yields statistically averaged nano-islands susceptibilities that do not correspond to a second order phase transition. The experimental susceptibility results for 2D Co nano-islands on Pt can be interpreted within our EFT Ising model without reference to a transition from a blocking state of the particle to a superparamagnetic behavior. The results for the different lattices are formally comparable, and demonstrate the robustness and general character of the model.     

Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method

In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analytically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green’s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose–Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose–Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lattices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the experimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 (2011)]. In square optical lattice, the emergence of peaks at \(\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)\) in the time-of-flight absorption pictures, which is believed to be a sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.     

Excitation of phase transitions in dipole lattices

Phase transitions in hexagonal lattices with three and four rows of dipoles arising as a result of the reorientation of different sets of dipoles by the external field have been studied. The conditions of the implementation of two types of symmetric phase transitions and the asymmetric transitions, when the configurations of the system to the left and to the right of the excitation region are different, have been established. Merging of two regions of the phase transitions has been considered. Unidirectional phase transitions, in which either the left or the right phase transition front propagates from the excitation region along the lattice, have been obtained in a lattice with four rows of dipoles. The variations of the total dipole moment of the system and the energy of the dipole-dipole interaction during the phase transitions have been given.     

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.     

Imaging of a vortex lattice transition in YNi2B2C by scanning tunneling spectroscopy

The vortex lattices in YNi2B2C under the magnetic fields H up to 3 T applied along both the a and the c axes have been studied by scanning tunneling spectroscopy at 4.2 K. The vortex lattice transition has been found to occur in different manners for H parallela and H parallelc; in H parallela a slightly distorted hexagonal vortex lattice has been found to transform to a nearly square one above 1.0 T with increasing H, while in H parallelc the transition occurs at a much lower field around 0.1 T. The unconventional steep increase of the quasiparticle density of states outside the vortex core has also been found well below H(c2).     

A mean—field approximation scheme containing the spatial parameter and its application to a surface—reaction—like cellular automaton model

Using an AB2 Surface-reaction-like cellular automaton model,we present a modified mean-field approximation scheme for describing some dynamic lattice models,in which a lattice freedom parameter N is introduced as a variable,We obtain the phase diagrams of the example model for linear,hexagonal,square and triangular lattices,and we reveal a second-order phase transiton which has not been found using using traditional approaches.