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We use the continued fraction formalism (CFF) to obtain the zz-component of the dynamical spin pair correlations of a transverse Ising model (TIM) in 2 D at T = ∞ for the first time. Our calculations suggest that the correlation function decays algebraically at long times as t-α, 1.5&lt;α&lt;2.2, which is slower than gaussian decay found for the corresponding dynamical correlation in 1 D. The calculations suggest that the corresponding dynamical correlation in 3 D is also likely to exhibit a power law decay. Our results compare favorably with the neutron scattering data on LiTbF4, for T&gt;Tc, an induced moment ferromagnet.

Department of Bioscience & Bioengineering

World University root node

Materials Research Society Symposium Proceedings

Long time dynamics of the transverse Ising model - comparison with data on LiTbF4

Structural and dynamic properties of a large class of intercalation compounds can be modelled by a collection of ions interacting via a screened Coulomb potential and subjected to the corrugation potential produced by the host atoms. In this paper we discuss the results of Molecular Dynamics simulation studies of the ground state structure of RbC24 and related systems focusing primarily on the micro-structure i.e. on the nature of the domains and domain walls.

Ionic overlayers on corrugated surfaces I: Structure

An extensive study on low temperature solid and high temperature liquid phases of stage 2 alkali-metal graphite intercalation compounds (GICs), as examples of two dimensional screened Coulomb (repulsive) systems on strongly corrugation modulated substrates, is presented using constant energy and constant temperature (Nosé) Molecular Dynamics (MD) simulations. We present pair correlation functions, static structure factors and snapshots of microscopic structures in the liquid phase, in the freezing region and in the solid phase. Average energy, diffusion constant and the number of disclinations are monitored as a function of temperature to track down the transition (freezing) region. We also find that the number density of the topological defects (such as dislocations and disclinations) decreases rapidly at the freezing transition. In the solid phase of RbC24 we find small triangular domains of x) Rb structure with welldefined domain walls consisting of (2x2) and (2x3x7) elemental plaquettes of Rb. These nanostructures provide a clear picture of the discommensurations (domain walls) and a consistent understanding of the X-ray diffraction measurements. Our simulation studies suggest a Periodic Domain Wall model to describe the low temperature solid phase structure of the alkali metal GIC's. This model explains the dominant features of the experimental X-ray structure factor. © 1993, Taylor & Francis Group, LLC. All rights reserved.

Molecular Simulation

Structural Properties of Stage-2 Alkali-Metal Graphite Intercalation Compounds: A Molecular Dynamics Study

Using molecular dynamics simulation we have investigated the melting properties of a 2-dimensional system of ions interacting through a screened Coulomb potential in the presence of a substrate. We focus on the role of the substrate potential in the melting transition. The physical system we study is the stage-2 graphite intercalation compound RbC24 and a related system RbC24.57 whose intercalant density differs from the former by a small amount. Our results reveal the nature of melting processes characteristic of periodic domain wall solids.

Ionic overlayers on corrugated surfaces II: Melting

The continued-fraction formalism demonstrates that the Laplace-transformed dynamical correlations can be expressed as infinite continued fractions (ICF's). We propose a generalization of the dynamical convergence method (GDCM) of J. Hong and M. H. Lee [Phys. Rev. Lett. 55, 2375 (1985)] of perturbatively evaluating insoluble ICF's when a closely related ICF is exactly soluble. The proposed method overcomes an existing limitation of the dynamical convergence method which involves accurate computing of ratios of small numbers. The limitations are surmounted by exploiting an "inversion" property of ICF's. The GDCM allows computationally fast and simple perturbative evaluation of insoluble ICF's with up to 10ξ, ξ≤6, levels of the insoluble ICF when a related ICF is soluble. The method appears to be appropriate for studies of asymptotic behavior of dynamical correlations described by slowly converging and nonconverging ICF's, which are otherwise insoluble, when closely related soluble ICF's exist. The desirable feature of the GDCM is that the computation times required to solve the ICF's are unrelated to the details of the convergence properties. The method has been applied to recalculate the dynamical-spin pair correlation of a recently studied classical XX spin cluster. This application is described in this work. © 1993 The American Physical Society.

Physical Review E

Asymptotic behavior of dynamical correlations via perturbative analysis of infinite continued fractions

By use of constant energy molecular dynamics simulations, we have investigated the melting and freezing transitions in a two-dimensional system consisting of a constant density of classical particles interacting with a repulsive screened Coulomb (Yukawa) potential. In particular, we have investigated the role of an incommensurate substrate corrugation potential of sixfold symmetry on these transitions by probing the temperature dependence of the bond orientational order parameter (ψ6) and the corresponding susceptibility (χ6). Other physical quantities such as energy, diffusion constant, and the density of local topological defects have been monitored through the transition region. In the absence of a corrugation potential the system shows a sharp melting transition. In the presence of a corrugation potential the transition temperature increases and the transition becomes smoother. In contrast to the corrugation-free case we find a broad peak in χ6 above the transition temperature. We interpret this behavior in terms of the melting of a domain-wall solid. The detailed nature of this smooth transition depends on the degree of incommensurability. Relevance of these results to stage-2 graphite intercalation compounds is discussed. © 1992 The American Physical Society.

Fulltext

Physical Review B

Melting of a repulsive screened Coulomb system in two dimensions: Effect of corrugation

Mori theory leads to in(finite) continued fractions [I(F)CFs] which upon inverse Laplace transformation (ILT) give the dynamical correlations in Hamiltonian systems. We propose a direct summation method to evaluate these ICFs, e.g., 1/[z+1/(z+...)], by replacing them with FCFs with poles L=102. Long-time dynamics is obtained upon an ILT of the ICF for 0 with being large. Our studies on dynamical correlations for boundary spins in S=1/2 XY chains agree very well with a recent exact solution for these correlations. © 1992 The American Physical Society.

Physical Review Letters

Long-time dynamics via direct summation of infinite continued fractions

We present a study on the nature of the dynamical on-site spin-pair correlation in an s=1/2 isotropic Heisenberg chain at T= using the Mori-Lee formalism for solving the Heisenberg equation of motion and the direct summation method of evaluating infinite continued fractions. Our results are consistent with existing short-time analyses and support a power-law decay of the spin-pair correlations. Our study reveals that the frequency spectra corresponding to the on-site dynamical correlations can be seen as consisting of a Gaussian central peak presumably arising from the XY part of the Hamiltonian and a second broad finite frequency peak, which probably arises from the Ising part of the Hamiltonian and is slightly shifted toward a higher frequency than the Ising frequency. © 1992 The American Physical Society.

Dynamical correlations in an s=1/2 isotropic Heisenberg chain at T=

The structure of domains and domain walls in the low-temperature solid phase of stage-2 alkali-metal graphite intercalation compounds is studied using molecular-dynamics (MD) simulation and a model potential obtained from fitting to the liquid structure data. For RbC24, we find small domains of (s 7 × s 7) structure containing mostly seven Rb atoms and with domain walls consisting of (2×2) and (2×3) elemental plaquettes. These nanostructures provide a clear picture of the discommensurations and a consistent understanding of the x-ray-diffraction measurements. Based on the simulation results, we propose a periodic domain-wall model that explains very well the dominant features of the x-ray structure factor for both RbC24 and CsC24 when we allow for small changes in the planar density. © 1992 The American Physical Society.

Domains and domain walls in graphite intercalation compounds

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. © 1992 Plenum Publishing Corporation.

Journal of Low Temperature Physics

Quantum spin dynamics of the transverse Ising model in two dimensions

It is shown that some of the simplest interacting many body systems exhibiting non-ergodicity necessarily satisfy certain identities involving their equilibrium multipoint static correlations. These identities may be useful in the study of model non-ergodic systems being analysed or simulated. Some examples of pertinent model non-ergodic systems are given to illustrate the material discussed. © 1992.

Physica A: Statistical Mechanics and its Applications

Aspects of non-ergpdicity in Hermitian systems

The Heisenberg equation of motion for the surface spin operator in a semi-infinite S=1/2 XY chain is exactly solved at infinite temperatures via the recurrence-relations method of Lee. It is found that the time evolution of the surface spin shows Bessel-like on-site relaxation that is drastically different from the corresponding Gaussian relaxation of a bulk spin. This difference is shown to be related to broken translational symmetry in the former case. The memory function and the random force for the surface spin is exactly determined. It is found that the surface spin dynamics is, in some sense, "harmonic" in nature. © 1991 The American Physical Society.

Exact solution of the Heisenberg equation of motion for the surface spin in a semi-infinite S=1/2 XY chain at infinite temperatures

The time evolution of a spin operator Sjx(t) in a nearest-neighbor S=1/2 semi-infinite XY chain is considered at T=. It is shown that the surface spin relaxes very differently compared to the subsurface spin, which already behaves like a bulk spin. The transition from surface to bulk dynamics is discussed using the recurrence-relations method of solving the Heisenberg equation of motion. © 1991 The American Physical Society.