Kinetics of domain wall pinning in an incommensurate Pb overlayer on a Cu(110) surface

We have used grazing incidence X-ray scattering to study the kinetics of domain wall pinning during the transition between an incommensurate phase and a domain wall glass phase. The growth of both domain wall density and domain size are described by power-laws. The results are discussed in the context of recent theoretical models of growth.     

Combination of temperature-programmed thermal desorption and laser-induced thermal desorption

The combination of temperature-programmed thermal desorption with heating rates of the order of 1 K s^–1 and laser-induced thermal desorption with of the order of 10¹⁰ K s^–1 has proved to be a suitable method to determine both the frequency factor v and the activation energy E _d of desorption. The systems Ni(110)/N₂ and Ni(110)/CO serve as examples.     

Gauge-invariant lattice gas for the microcanonical Ising model

We introduce a lattice gas for particles with discrete momenta (1, 0, –1) and local deterministic microdynamics, which exactly reproduces Creutz's microcanonical algorithm for the ferromagnetic Ising model. However, because of the manifest gauge invariance of our variables, both the Ising ferromagnetic and spin-glass systems share precisely the same dynamics with different initial conditions. Additional conservation laws in the 1D Ising case result in a completely integrable system in the limit of zero or unbounded demon energy cutoff. Numerical investigations of ergodicity are presented for the pure Ising lattice gas in one and two dimensions.     

Angle and speed distributions of hydrogen desorbing thermally from metal surfaces

On the basis of the theory developed in a previous paper (Part I), the angle and speed distributions of D₂ molecules desorbing thermally from the Ni(111) surface are numerically calculated in the present paper (Part II). The dynamical motion of the activated complex of the recombinative desorption process is calculated by using a model potential surface, which involves a few parameters introduced to describe the necessary features of the potential surface at the transition state. Numerical calculations are carried out, and the results show that the present dynamical theory reproduces very well a variety of the characteristic features of the experimental results, e.g., sharply focused angular distribution, mean translational energy lower than 2k _B T at grazing angle, and the non-Maxwellian profile of the TOF distribution.     

Kinetic Ising model: Some exact solutions

Exact expressions for the response functions of kinetic Ising models are reported. These results valid for magnetisation in one dimension are based on a general formalism that yield the earlier results of Glauber and Kimball as special cases.     

Kallen–Lehman approach to 3D Ising model

A “Kallen–Lehman” approach to Ising model, inspired by quantum field theory à la Regge, is proposed. The analogy with the Kallen–Lehman representation leads to a formula for the free-energy of the 3D model with few free parameters which could be matched with the numerical data. The possible application of this scheme to the spin glass case is shortly discussed.     

Angle and speed distributions of hydrogen desorbing thermally from metal surfaces

A quantum theoretical treatment of the angle and speed distributions of recombinatively desorbing hydrogen from metal surfaces is proposed. The desorption rate is discussed in the framework of the transition state theory. The recombinative reaction process of hydrogen due to thermal activation leads to the formation of an activated complex in the transition state. In the vicinity of a saddle point on a three-dimensional potential energy surface, the translational motion of the activated complex in the direction perpendicular to the metal surface is accompanied by its center-of-mass vibrational motion parallel to the metal surface. In order to carry out the quantum mechanical calculation, the potential surface is replaced by a simplified model potential, which provides a square potential barrier along the surface normal. It is shown that, on leaving the potential barrier, the activated complex is reflected by the boundary of the potential barrier with a certain probability and, at the same time, the center-of-mass modes of vibration with frequencies v ₁ and v ₂ are coupled with the translational motion along the surface normal. Vibrational wave functions in the momentum representation are used to calculate the transmission coefficient, which is incorporated into the conventional rate formula. The angle-dependent speed distributions of desorbing molecules are derived from the rate formula.     

Clusters and Ising droplets in the antiferromagnetic lattice gas

A definition of clusters of particles and holes with antiferromagnetic order is given for a lattice gas with coupling constant K < 0. In two dimensions it is shown that the Ising antiferromagnetic critical line is also a percolation line if P_b = 1 - exp(-|K|/2). Along this line these clusters called “droplets” diverge with Ising exponents.     

Dynamical anomalies in physisorbed films of Sn(CH3) and Fe(CO)5 on graphite basal plane

Several dynamical properties of Sn(CH₃)₄ and Fe(CO)₅ molecules physisorbed on graphite, are influenced by the form of two-dimensional solid growth. As inferred from Mössbauer results, at temperatures where the molecules form solid superstructures and below monolayer coverages, abnormal changes are observed in the mean squared displacement of the molecules. It is suggested that these dynamical anomalies are associated with substrate-adsorbate registry.     

Steps,facets and nanostructures: investigations of Cu (11n) surfaces

Step structure and dynamics and adsorbate-induced reconstruction of stepped surfaces are useful features for investigating fundamental surface phenomena and their practical consequences. In this respect, vicinal Cu (11n) surfaces with n=3, 5 and 9 were studied by scanning tunneling microscopy (STM) at 300 K. While the regular monoatomic steps fluctuate for Cu (119), they are apparently stabilized for n≤5 by their strong repulsive interaction and this leads to a very low kink activity. In addition to the regular steps, the formation of double steps was observed as a particular phenomenon on those surfaces. These double steps determine the dynamic behavior at room temperature. By applying existing models for the fluctuations of the step positions in space and time, the formation energy for kinks at these double steps was determined to be 0.16 eV for Cu (115). According to this evaluation, diffusion along step edges is the dominating mass-transport mechanism. A model for the structure of the double steps and for the atomic displacement processes necessary for kink migration at these steps is presented. Complete faceting is observed for these surfaces upon oxygen adsorption at elevated temperatures (around 500 K) and was studied in detail for n=5 and 9. Both surfaces reconstruct into two types of {104} facets and a third facet, the orientation of which is determined by the macroscopic crystal orientation. The facet size is governed by the formation kinetics and can be controlled by varying the crystal temperature or the oxygen partial pressure. The formation kinetics is discussed as a nucleation and growth process and the relevant parameters are given. Facets within a range of size between 5 nm and 100 nm could thus be produced. They remained stable at ambient atmosphere, up to about 620 K, and also if covered by additional metal layers such as Ni. Received: 1 June 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002     

Buckling in a solid Langmuir monolayer: light scattering measurements and elastic model

Above a surface pressure threshold , we detect a buckled state in the low temperature solid phase of a phospholipid monolayer spread at the air-formamide interface. Stable ripples are observed with a Brewster angle microscope, and light scattering provides measurements mNm^-1, wavelength m and amplitude of a few nm for the deformation. A model, coupling the monolayer thickness and elongation, and consistent with the monolayer texture, is also presented. Received: 18 August 1997 / Revised: 9 December 1997 / Accepted: 29 January 1998     

Study of Ising model on the rectangular-triangular lattice

The Ising model is studied on a new type of lattice which is named the rectangular-triangular lattice. The critical temperature for the ferromagnetic lattice is calculated exactly and it is shown that the antiferromagnetic lattice does not order at any temperature. Ground state properties are investigated and some features of frustration on the antiferromagnetic Ising lattice outlined.     

Susceptibility of the Kagomé lattice Ising model

We explicitly calculate the zero-field magnetic susceptibility of the anisotropic Kagomé lattice Ising model on two different varieties of the parameter space. One of them is the limitH=0 of the solubility condition, obtained in a previous paper by Giacomini, for the model with magnetic field. The other one is the disorder variety of the model, for which a dimensional reduction occurs. These varieties do not contain any nontrivial critical behavior of the model. A functional relation is also established, which relates the zero-field susceptibility for ferromagnetic and competing interactions.     

Statics and kinetics at the nematic-isotropic interface in porous media

We extend the random anisotropy nematic spin model to study nematic-isotropic transitions in porous media. A complete phase diagram is obtained. In the limit of relative low randomness the existence of a triple point is predicted. For relatively large randomness we have found a depression in temperature at the transition, together with a first order transition which ends at a tricritical point, beyond which the transition becomes continuous. We use this model to investigate the motion of the nematic-isotropic interface. We assume the system to be isothermal and initially quenched into the metastable régime of the isotropic phase. Using an appropriate form of the free energy density we obtain the domain wall solutions of the time-dependent Ginzburg-Landau equation. We find that including a random field leads to smaller velocity of the interface and to larger interface width. Received 12 November 1998 and Received in final form 15 March 1999     

Square lattice variational approximations applied to the Ising model

The variational method developed by Baxter is applied to the zero-field Ising model on the square lattice. The problem is simplified to that of solving a relatively small system of nonlinear equations. The estimates to the spontaneous magnetization and the critical temperature from the sequence of variational approximations are obtained. The results converge rapidly to the exact ones. They exhibit a crossover phenomenon and satisfy a scaling relation.     

The antiferromagnetic Ising model for a bilayer Bethe lattice

The totally antiferromagnetic Ising model is analyzed on a bilayer Bethe lattice in detail by studying the order-parameters, response functions, i.e. susceptibility and specific heat, and free energy by using the recursion relations in a pairwise approach. The ground state phase diagrams of the model are also obtained on the (_J2/|_J1|,_J3/q|_J1|)$(J_2/|J_1|,J_3/q|J_1|)$ plane for given values of H/q|_J1|$H/q\left|J_1\right|$ and on the (H/q|_J1|,_J3/q|_J1|)$(H/q|J_1|,J_3/q|J_1|)$ plane for given _J2/|_J1|$J_2/\left|J_1\right|$. As a result, we have obtained the temperature-dependent phase diagrams for various values of the coordination number q   on the (_J3/|_J1|,kT/|_J1|)$(J_3/|J_1|,\mathit{kT}/|J_1|)$ and (H/|_J1|,kT/|_J1|)$(H/|J_1|,\mathit{kT}/|J_1|)$ planes for given values of the rest of the system parameters.     

On the Ising model for the simple cubic lattice

The Ising model was introduced in 1920 to describe a uniaxial system of magnetic moments, localized on a lattice, interacting via nearest-neighbour exchange interaction. It is the generic model for a continuous phase transition and arguably the most studied model in theoretical physics. Since it was solved for a two-dimensional lattice by Onsager in 1944, thereby representing one of the very few exactly solvable models in dimensions higher than one, it has served as a testing ground for new developments in analytic treatment and numerical algorithms. Only series expansions and numerical approaches, such as Monte Carlo simulations, are available in three dimensions. This review focuses on Monte Carlo simulation. We build upon a data set of unprecedented size. A great number of quantities of the model are estimated near the critical coupling. We present both a conventional analysis and an analysis in terms of a Puiseux series for the critical exponents. The former gives distinct values of the high- and low-temperature exponents; by means of the latter we can get these exponents to be equal at the cost of having true asymptotic behaviour being found only extremely close to the critical point. The consequences of this for simulations of lattice systems are discussed at length.