Zhi-Xiong Cai

Dynamic structure factor of the transverse Ising model

We report the first analytic study of real time and frequency dependent behaviour at T= infinity of the 2D square lattice transverse Ising model. Our study, along with known results in the 1D case, in the mean field or infinity D case and in other studies, helps understand the experimentally obtained longitudinal dynamic structure factor of the induced moment ferromagnet LiTbF4 studied by Youngblood et al., and is consistent with the studies of Kotzler et al.

Quantum spin dynamics of the transverse Ising model in two dimensions

We use the method of recurrence relations to obtain the time-dependent spin correlation function of the Ising model in a transverse field in 2D. We find that the correlation function decays algebraically at long times as t−α where α ≤2.2. This is to be contrasted with the 1D case where the decay is Gaussian. We expect that in 3D the dynamical correlation will also exhibit a power law decay. Our results can be used to understand the experimental shape functions for the induced moment in LiTbpY1−pF4.

Numerical simulations of flux-line lattices in layered superconductors

Abstract A model of the effective interaction between the magnetic flux-lines in a layered superconductor is derived from the Lawrence–Doniach model. We show analytically that the intralayer interaction energy can be evaluated using the Ewald summation technique. To illustrate the usefulness of the simulation technique, the isothermal shear modulus c 66 of flux-line lattices with various values of the interlayer coupling strength was obtained with a Langevin dynamics simulation.

Structure of twin boundaries in La2 − xBaxCuO4

Abstract The structure of the twin boundary in the low-temperature-orthorhombic (LTO) phase of La2 − xBaxCuO4 is studied using a Landau-type free-energy model which reproduces the x − T phase diagram. We find that the twin boundaries that have the lowest free energy are those with low-temperature-tetragonal (LTT) structure in the center of the domain walls. Near the LTT-to-LTO phase-transition temperature, both the width as well as the density of the twin boundaries increase with decreasing temperature.

Simulation study of grain growth in layered materials application to YBa2Cu3O7-δ ceramics

Abstract We propose a simple lattice model which takes into account the anisotropy of grain formation energy to study the grain growth of layered materials such as polycrystalline superconducting cuprates. The anisotropic parameter in this model is estimated in the case of YBa2Cu3O7-δvia a semi-empirical theory for surface energy anisotropy. Monte Car10 simulation shows that the anisotropy of grain formation energy causes abnormal grain growth in which large elongated grains grow at the expense of fine matrix grains. The evolution with time of parameters characterizing the grain sizes and shapes have been calculated. In general, the results agree very well with experimental observation.

Domain structure in two-dimensional lattices with randomly distributed pinning centers: Application to type-II superconductors

We present a molecular-dynamics-based study on certain structural features of disordered two-dimensional lattices of N particles with screened Coulomb interactions which are placed on rigid substrates with N{sub p} randomly distributed Gaussian pinning centers. We find that over a wide temperature range, for N{sub p}=N and for various pinning intensities A{sub p}, the lattice structures are typically described by domains of triangular-lattice-like regions punctuated by domains of clustered topological defects. Our calculations reveal that as A{sub p} increases, sizable triangular-lattice-like regions coexist with increased topological defect densities. This result suggests that the particles remain correlated even at strong pinning regimes. Its implications are discussed in relation to recent experiments on heavy-ion-irradiated high-temperature superconductors and the assumptions used in various flux pinning theories of type-II superconductors. {copyright} {ital 1998} {ital The American Physical Society}

Isothermal elastic constants of flux-line lattice in layered superconductors

A model of the effective interaction between the magnetic flux-lines in a layered superconductor is derived from the Lawrence–Doniach model. We show analytically that the intralayer interaction energy can be evaluated using the Ewald summation technique. The melting of flux line lattices is studied using Langevin dynamics simulation of the model with various values of interlayer coupling strength and pinning intensities. The thermal fluctuation terms of the isothermal shear modulus are found to increase sharply at the melting transition temperature for systems with or without pinning, while the structural order parameters were close to zero at all temperatures for systems with strong pinning. The melting of the pinned flux-line lattice is discussed in the context of its elastic properties.

2 D Lattices on Substrates with Randomly Distributed Pinning Centers: A Possible Scaling Law for Domain Sizes

The authors consider 2D lattices which are disordered by an external field, in this case by a dense, random distribution of attractive pinning centers of an underlying substrate. The preferred configuration of the 2D system with screened-Coulomb two-body interactions and a fixed number of particles is a triangular lattice configuration. The pinning centers strongly affect the triangular lattice configuration. By keeping the location and the density of the pinning centers fixed, they study the effects of pinning strength on the structural properties of the lattice. They find that the strongly disordered lattice prefers to form irregular domains of size s which are composed entirely of topological defects. The distribution of sizes of these domains, D(s) suggest that s{sup {minus}{tau}} for sufficiently large s. The results are consistent with {tau} {ge} 2 in the solid phase and {tau} < 2 in the liquid phase. They present a general argument in support of the findings and suggest that the physics which dictates the structure of 2D lattices on substrates with randomly distributed pinning centers is the same as that for a broad range of problems in which an external field strongly influences the behavior of an interacting physical system.

A model of the consecutive structural phase transitions in La2-xBaxCuO4

Abstract A simple lattice-dynamical model is constructed with the parameters chosen to fit the energy surface of the superconducting La 2- x Ba x CuO 4 , x ∼0.1, derived from first-principles calculations. The model possesses many of the features occuring in the consecutive structural phase transitions in solids with the layered perovskite structure. We find that the anharmonicity in the model causes a vibrational-entropy-driven first-order phase transition from the LTT to the LTO structure at low temperatures. The high-temperature LTO to HTT transition is found to be of the order-disorder type and is continuous.

Theory on the Structure of Twin Boundaries in La 2− x ,Ba x CuO 4

The structure of the twin boundary in the low-temperature-orthorhombic phase of La 2− x Ba x CuO 4 is studied using a Landau-type free energy model which reproduces the x − T phase diagram. The La 2− x Ba x CuO 4 compound has a body-centered tetragonal (HTT) structure at high temperatures. Upon cooling it undergoes a structural phase transition to a low-temperature orthorhombic structure (LTO structure) which is caused by the tilting of the CuO 6 octahedra about the (110) and ( 1 10) directions. Depending on the doping level x , the LTO structure may go through another phase transition at an even lower temperature to a low-temperature tetragonal phase (LTT phase). We find that the existence of LTT phase greatly changes the characteristics of the twin boundary in the LTO phase. LTT phase exists at twin boundaries of the LTO phase at temperatures well above the LTT to LTO transition temperature.