Monte Carlo simulation of the percolation process caused by the random sequential adsorption of k-mers on heterogeneous triangular lattices

Mixed site-bond percolation is studied for a random sequential adsorption process of k-mers on heterogeneous lattices with variable connectivity by means of Monte Carlo simulation. The percolation phase diagrams are built to render evidence about complex structures. Critical exponents are also calculated to show that the universality class corresponding to ordinary percolation in two dimensions is preserved.     

A vectorizable random lattice

We describe a family of random lattices in which the connectivity is determined by the Voronoi construction while the vectorizability is not lost. We can continuously vary the degree of randomness so in a certain limit a regular lattice is recovered. Several statistical properties of the cells and bonds of these lattices are measured. We also study anisotropy effects on the numerical solution of the Laplace equation for varying degrees of randomness.     

镶嵌正方晶格上Gauss模型的相图

利用等效变换和自旋重标相结合的方法, 研究了镶嵌正方晶格上的Gauss模型. 研究 发现, 该系统可以变换为正方晶格上具有最近邻和次近邻相互作用的Gauss系统, 由此严格求得了镶嵌正方晶格上Gauss模型的临界温度, 得到了该系统的精确相图.     

A Remark on the Notion of Robust Phase Transitions

We point out that the high-qPotts model on a regular lattice at its transition temperature provides an example of a nonrobust—in the sense recently proposed by Pemantle and Steif—phase transition.     

The Bethe lattice spin glass revisited

So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization. Received 27 September 2000     

Variational calculations on the energy levels of graphene quantum antidots

The critical properties of the two-dimensional Ising and Blume-Capel model on directedsmall-world lattices with quenched connectivity disorder are investigated. The disordered system is simulated by applying the Monte Carlo method with heat bath update algorithm and histogram re-weighting techniques. The critical temperature, as well as the critical exponents are obtained. For both models the critical parameters have been obtained for several values of the rewiring probability p. It is found that these disorder systems do not belong to the same universality class as two-dimensional ferromagnetic model on regular lattices. In particular, the Blume-Capel model, with zero crystal field interaction, on a directedsmall-world lattice presents a second-order phase transition for p < p _c , and a first-order phase transition for p > p _c , where p _c  ≈ 0.25. The critical exponents for p < p _c are different from those of the same model on a regular lattice, but are identical to the exponents of the Ising model on directedsmall-world lattice.     

Global invariants and equilibrium states in lattice gases

It is now well known that, in addition to the physical conserved quantities, lattice gases also have other unphysical ones related to the discretization of their phase space. From an abstract point of view a lattice gas can be considered like a full discrete Markov processL and these spurious conserved quantities yield the existence of a nonspatially homogeneous equilibrium state forL ^k. We show that a particular set of these conserved quantities is of special interest: Its elements will be called regular. These regular invariants are simply built from the local ones and their projection on each node is always a locally conserved quantity. Moreover, for most models they are one-to-one related to the Gibbs states ofL ^k which remain factorized. It turns out that all the classical known spurious invariants are regular and one can exhibit simple conditions to build models with only regular invariants. For the latter it is then justified to determine the transport coefficients of the locally conserved densities with the Green-Kubo procedure.     

STM analysis of triosmium carbonyl cluster adsorption at HOPG

The study of metallic carbonyl clusters as precursors in tailoring the heterogeneous metal catalysts has been of great importance. The catalytic nature of the adsorbed clusters in thin film form depends on the chemical properties of the substrate used. The metal-support interaction will determine various properties such as the surface morphology, adsorption features and the structural orientations. We report a scanning tunneling microscopy (STM) study of an osmium carbonyl cluster (Os₃(CO)₁₁(NCCH₃)) adsorbed on highly oriented pyrolytic graphite (HOPG). STM measurements showed that the osmium carbonyl cluster interacts with HOPG in such a way that it adsorbs on the basal plane showing regular lattice structure, whereas the axial planes of the HOPG surface shows no ordered structure. The regular cluster lattice structure of the carbonyl cluster on the basal plane of the graphite has lattice parameters of a=1.4 nm and b=1.5 nm. We believe that the regular orientation of the cluster indicates a monolayer adsorption of the cluster on the graphite basal planes. Scanning tunneling spectroscopy (STS) measurements also indicated an insulating behavior for the cluster molecules on HOPG, with a significant energy gap value of ca. 300 mV. The cluster interaction at the active sites, i.e. axial planes of the graphite, was also observed by in situ STM measurements.     

Clathrate hydrates modelled with classical density functional theory coupled with a simple lattice gas and van der Waals-Platteeuw theory

Predicting clathrate hydrate phase equilibria is of interest in the area of natural gas exploitation. This proof of concept study presents the application of a simple lattice gas model and classical density functional theory coupled with van der Waals-Platteeuw theory to predict clathrate hydrate phase equilibria for several different hydrate-forming gas species. The dissociation pressure curve is predicted using adsorption isotherms predicted for the gas species in the crystal hydrate lattice. Comparisons are made between predicted phase equilibria (and other properties) and available experimental data.     

The dimer-trimer model for heterogeneous catalysis

We study a dimer-trimer lattice model for heterogeneous catalysis for the reaction 1/2A₂+1/3B₃AB. The A₂ and B₃ particles require two and three active sites for their adsorption onto the lattice, respectively. The model is unusual in that it possesses an infinite number of absorbing states whereby the lattice is poisoned and reactions must stop. Previously studied models have only two absorbing states. In one dimension, the lattice poisons with mostly dimers and a few trimers even at vanishingly small dimer-adsorption probabilities and there is a discontinuity when this probability is zero. On the triangular lattice, the poisoned phases consist of only one component and vacancies, and the phase diagram is similar to that of the monomer-dimer model of Ziff, Gulari, and Barshad. However, the second-order transition belongs to a different universality class than Reggeon field theory, contrary to previous models. Finally, we present results for the Kagomé lattice, for which the poisoned phases consist of two components due to its smaller connectivity.     

Regular phases of atomic hydrogen chemisorbed on graphite

The crystalline orbital-NDO method is applied to regular chemisorption of atomic hydrogen on a graphite monolayer and further features of this method are discussed, especially as concerning truncation in direct lattice sums. Particular attention is given to the balance of Coulomb terms at relatively short distances. The surface phases allowed by the graphite symmetry for hydrogen atoms chemisorbed at equivalent positions in the hydrogen/carbon atomic ratios $\text{1}\text{2}$, $\text{1}\text{1}$ and $\text{3}\text{2}$ are discussed in terms of adsorption energy and electron charge distribution, duly taking into account the substrate relaxation. The greatest adsorption energy is shown by the $\text{1}\text{1}$ phase, with formation of typical CH chemical bonds. An even greater stability is shown by a phase having the same overall composition in which the graphite monolayer is attacked on both sides by atomic hydrogen, giving rise to a “chair” structure of carbon rings similar to that in cyclohexane. Such a phase could be of interest for inclusion and exfoliation processes possibly occurring in graphite demolition.     

Mott insulator-superfluid phase transition in a detuned multi-connected Jaynes-Cummings lattice

The connectivity and tunability of superconducting quantum devices provide a rich platform to build quantum simulators and study novel many-body physics. Here we study quantum phase transition in a detuned multi-connected Jaynes-Cummings lattice, which can be constructed with superconducting circuits. This model is composed of alternatively connected qubits and cavity modes.Using a numerical method, we show that by varying the detuning between the qubits and the cavities, a phase transition from the superfluid phase to the Mott insulator phase occurs at commensurate fillings in a one-dimensional array. We study the phase transition in lattices with symmetric and asymmetric couplings, respectively.     

Bond breaking coupled with translation in rolling of covalently bound molecules

The response of a C60 molecule to manipulation across a surface displays a long range periodicity which corresponds to a rolling motion. A period of three or four lattice constants is observed and is accompanied by complex subharmonic structure due to molecular hops through a regular, repeating sequence of adsorption states. Combining experimental data and ab initio calculations, we show that this response corresponds to a rolling motion in which two of the four Si-C60 covalent bonds act as a pivot over which the molecule rotates while moving through one lattice constant and identify a sequence of C60 bonding configurations that accounts for the periodic structure.     

Diffusion of adsorbates on random alloy surfaces

In this work the diffusion of non-interacting adsorbates on a random AB alloy surface is considered. For this purpose a simple cubic (sc), body-centered cubic (bcc) or face-centered cubic (fcc) auxiliary metal lattice is introduced. The auxiliary lattice is truncated parallel to its (100) plane in such a way that the fourfold hollow positions of the metal surface form a regular net of adsorption sites with square symmetry. The adsorption energy of each adsorption site is determined by its own environment, i.e. by the numbers of direct A or B neighbors. The Monte-Carlo method has been utilized to simulate surface diffusion of adsorbates on such energetically heterogeneous alloy surfaces and to calculate the tracer, jump and chemical diffusion coefficients. The chemical diffusion coefficient was calculated via two different approaches: the fluctuation and the Kubo-Green method. The influence of energetical heterogeneities on the surface diffusion is largely pronounced at low temperatures and low surface coverages, where most of the adatoms are trapped by deep adsorption sites. It was found that at low temperatures the sequential occupation of the different types of adsorption sites can be observed. Received: 24 October 1997 / Accepted: 17 December 1997     

Lattice-gas model of multiple layer adsorption

The phase diagram for a lattice-gas model of physical adsorption on a homogeneous substrate has been calculated in a mean-field approximation. The first-order phase transitions corresponding to the addition of successive layers terminate in individual critical points as the temperature increases. The critical temperatures of successive layers increase, monotonically with layer number, from the critical temperature of the two-dimensional lattice gas to that of the bulk three-dimensional lattice gas. This last feature is probably an artifact of the mean-field approximation.     

Quantum Monte Carlo investigations of adsorption energetics on graphene

We have performed calculations of adsorption energetics on the graphene surface using the state-of-the-art diffusion quantum Monte Carlo method. Two types of configurations are considered in this work: the adsorption of a single O, F, or H atom on the graphene surface and the H-saturated graphene system (graphane). The adsorption energies are compared with those obtained from density functional theory with various exchange-correlation functionals. The results indicate that the approximate exchange-correlation functionals significantly overestimate the binding of O and F atoms on graphene, although the preferred adsorption sites are consistent. The energy errors are much less for atomic hydrogen adsorbed on the surface. We also find that a single O or H atom on graphene has a higher energy than in the molecular state, while the adsorption of a single F atom is preferred over the gas phase. In addition, the energetics of graphane is reported. The calculated equilibrium lattice constant turns out to be larger than that of graphene, at variance with a recent experimental suggestion.     

TheO(3) non-linear σ-model on a 2 dimensional random lattice

TheO(3) σ-model on a 2-dimensional random lattice is studied numerically. The comparison of the continuum behaviors of the model on both random and regular lattices is carried out. It is shown that both lattices have the same continuum limit of the model, and the random lattice seems not to have the advantage of the wider scaling window compared to the same sized regular square lattice.     

The Marginally Stable Bethe Lattice Spin Glass Revisited

Bethe lattice spins glasses are supposed to be marginally stable, i.e. their equilibrium probability distribution changes discontinuously when we add an external perturbation. So far the problem of a spin glass on a Bethe lattice has been studied only using an approximation where marginal stability is not present, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a marginally stable solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non-perturbative approach to the Bethe lattice spin glass problem using approximations that should be hopefully consistent with marginal stability.     

TheO(3) non-linear σ-model on a 2 dimensional random lattice

TheO(3) σ-model on a 2-dimensional random lattice is studied numerically. The comparison of the continuum behaviors of the model on both random and regular lattices is carried out. It is shown that both lattices have the same continuum limit of the model, and the random lattice seems not to have the advantage of the wider scaling window compared to the same sized regular square lattice.