Dimer problem solved by Vdovichenko's method

The dimer problem on a two-dimensional lattice is reduced to a problem of random walks on the lattice, and then the latter problem is solved by the method which Vdovichenko developed in order to derive an exact expression for the partition function of the Ising model on a two-dimensional lattice. The result for the generating function is identical to the usual result for the general lattice. For loose-packed lattices such as the square and the honeycomb lattice on a torus, it takes the form of a linear combination of four determinants, where no problem of determining signs occurs.     

Self-assembling and phase coexistence of SW trimers as complex amphiphile analogues. I. Simulations

We analyse by discrete molecular dynamics the self-assembly of SW trimer particles that contain a different number of attractive and repulsive spheres. They also have different geometries: linear, obtuse, rectangular and equilateral. We identify that some of these molecules exhibit liquid–vapour equilibria while others do not. For all of them, we show the morphological phase diagram built up from the different supra-molecular structures formed by each type of trimer. We simulated 14 different systems with a total of 321 states. The main features of the supra-molecular structures depend only on the composition and geometry of the trimer: triple SW trimers do not form supra-structures, double SW trimers and single SW trimers form monolayers, bilayers and worm-like micelles. The liquid–vapour coexistence properties are also exhibited. These trimers can be used to model complex amphiphiles beyond the standard ones, such as the Gemini and the Bola surfactants as well as colloidal particles.     

Fermionic Representation of Two-Dimensional Dimer Models

Dimer models in two dimensions give rise to well-known statistical lattice problems, which can be exactly solved by the same combinatorial techniques associated with the Ising model and which have been used to account for the phase transitions in a number of physically interesting systems. More recently, dimer models have been regarded as classical limits of the quantum ground state of some antiferromagnetic systems. We then revisit an early transfer-matrix calculation for the dimer model on the simple square lattice. We write a spin representation for the transfer matrix associated with the canonical partition function of two paradigmatic dimers models, on the 4–8 lattice, with an Ising-type transition, and on the brick lattice, with a peculiar commensurate–incommensurate transition. Using standard techniques, the problem is reduced to the calculation of the eigenvalues of a system of free fermions.     

金纳米环双体尺寸和耦合效应对表面等离子体共振特性的影响

采用离散偶极子近似方法系统地研究了金纳米环双体的消光光谱及其电场分布. 计算结果表明, 金纳米环双体在耦合作用下的共振消光峰对应着不同振动模式, 改变金纳米环双体的排列方式、 间距和尺寸大小, 其表面等离子体共振消光峰发生红移或蓝移. 因此可以通过对金纳米环双体结构参数和排列方式的设定, 调节其表面等离子体共振消光峰的位置. 电场分布表明, 水平排列的金纳米环双体较单个金纳米环产生更强的局部表面增强电场. 适当的小间距, 较大的内外半径的金纳米环水平阵列更适合做表面增强拉曼散射的衬底, 在生物分子检测等领域具有潜在的应用.     

The Interaction of Collinear Gaps of Arbitrary Charge in a Two Dimensional Dimer System

The correlation of gaps in dimer systems was introduced by Fisher and Stephenson (Phys Rev 132:1411–1431, 1963), who looked at the interaction of two monomers generated by the rigid exclusion of dimers on the closely packed square lattice. In previous work we considered the analogous problem on the hexagonal lattice, and we extended the set-up to include the correlation of any finite number of monomer clusters. For fairly general classes of monomer clusters we proved that the asymptotics of their correlation is given, for large separations between the clusters, by a multiplicative version of Coulomb’s law for 2D electrostatics. However, our previous results required that the monomer clusters consist (with possibly one exception) of an even number of monomers. In this paper we determine the asymptotics of general defect clusters along a lattice diagonal in the square lattice (involving an arbitrary, even or odd number of monomers), and find that it is given by the same Coulomb law. We also obtain a conceptual interpretation for the multiplicative constant as the product of the correlations of the individual clusters.     

Phase separation and flux quantization in the doped quantum dimer model on square and triangular lattices

The doped two-dimensional quantum dimer model is investigated by numerical techniques on the square and triangular lattices, with significantly different results. On the square lattice, at small enough doping, there is always a phase separation between an insulating valence-bond solid and a uniform superfluid phase, whereas on the triangular lattice, doping leads directly to a uniform superfluid in a large portion of the resonating-valence-bond (RVB) phase. Under an applied Aharonov-Bohm flux, the superfluid exhibits quantization in terms of half-flux quanta, consistent with Q=2e elementary charge quanta in transport properties.     

Tracer diffusion and correlations in ordered adsorption systems with defect-controlled transport mechanisms

In this study we develop a theory of tracer diffusion in 2D lattice-gas systems with strongly repulsive nearest neighbor interactions. The study is performed for a square lattice in the vicinity of half monolayer coverage. In this case the lattice gas forms a highly-ordered c phase. The adatom kinetics is reduced to the problem of random walks of long-living structural defects. The correlated motion of tracer-defect pairs is considered. Equations for correlation functions of tracer-vacancy, tracer-excessive adatoms and tracer-dimer pairs are derived and solved in terms of microscopic jump probabilities of defects. The solutions are exact in the case of dominant single defect transport mechanisms. In the case of dimer transport we applied the approximation of short-range correlation length. The values obtained for the correlation factor are in good agreement with the results of computer simulations in the over-stoichiometric range, while for sub-stoichiometric coverages the agreement is not very good. Received 20 September 1999 and Received in final form 14 April 2000     

Calculation of absolute electron-impact ionization cross-sections of dimers and trimers

We report calculations of the electron-impact ionization cross-sections of selected dimers (homonuclear diatomic molecules) and trimers (homonuclear triatomic molecules) using a method which relies only on macroscopic quantities in conjunction with a “defect concept”. The empirically determined defect describes the deviation of the cluster (dimer, trimer) cross-sections from a simple linear dependence on the cluster size. We compare the calculated cross-sections to experimental data for the dimers S₂ and F₂ and the trimer O₃ and we present predictions for the ionization cross-sections of Br₂, I₂, C₂ and C₃ for which no experimental data are available. Lastly, we extend the method to the calculation of ionization cross-sections for the fullerenes C₆₀ and C₇₀. Received 6 December 1999 and Received in final form 10 April 2000     

Single-crystal structural study of the pressure-temperature-induced dimerization of C<Subscript>60</Subscript>

We present a study by Raman spectroscopy and X-ray diffraction/diffuse scattering of C₆₀ single-crystals treated at high-pressure and high-temperature. This allowed us to obtain structural information on the C₆₀ dimer state which can be considered as an intermediate state in the polymerization process. In the 1-6 GPa pressure range the crystals are primarily formed of dimers with additional minor fractions of monomers, 1D and 2D polymers, as shown by the analysis of the Raman spectra. The dimers are disordered within an average cubic lattice derived from that of the monomer. Single-crystal diffraction patterns reveal a characteristic diffuse scattering intensity distribution which has been simulated by calculating the diffuse scattering produced by dimer and trimer model structures. Satisfactory agreement is obtained for random positional and orientational disorder of the C₆₀-C₆₀ dimers although a small concentration of similarly disordered trimers is likely. In a first approximation the dimer/trimer disorder can be considered as random but various inter-dimer correlations are probably present, as discussed.Received: 3 October 2003, Published online: 19 February 2004PACS: 61.48. + c Fullerenes and fullerene-related materials - 61.43.Bn Structural modeling: serial-addition models, computer simulation - 78.30.Na Fullerenes and related materialsT. Wågberg: Present address: Groupe de Dynamique des Phases Condensées, Université Montpellier II, Place E. Bataillon, CC026, 34095 Montpellier, France     

Real space renormalization group with effective interactions: applications to 2-D spin lattices

The Blochs theory of effective Hamiltonians has been used to improve the Real Space Renormalization Group approach. The effective interactions between elementary blocks of a periodic lattice can be extracted from the knowledge of the spectrum of the dimers or trimers of blocks. The potentialities of the method are illustrated on a series of quasi 1-D and 2-D problems. The spin gap of two-leg ladders is calculated and an estimate of the impact of ferromagnetic couplings between two-leg ladders on the gap is presented. The method satisfactorily identifies the phase transitions in the 1/5-depleted square lattice as well as in the spin-frustrated Shastry-Sutherland lattice. The J ₂/J ₁ checkerboard lattice is studied and a location of the phase transition between the Néel phase and the dimer phase is proposed.Received: 11 June 2004, Published online: 30 September 2004PACS: 71.10.-W Theories and models of many-electron systems - 71.15.Nc Total energy and cohesive energy calculations - 75.10.-b General theory and models of magnetic ordering     

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.     

Low-temperature phases obtained by linear programming: An application to a lattice system of model chiral molecules

A convenient, Peierls-type approach to obtain low-temperature phases is to use the method of an m-potential. In this paper we show that, for more complex systems where it may be rather difficult to rewrite the Hamiltonian as an m-potential and whose configurations are subject to linear constraints, the verification of the Peierls condition can be reformulated as a linear programming problem. Before introducing this novel strategy for a general lattice system, we compare it with the m-potential method for a specific model molecular system consisting of an equimolar mixture of a chiral molecule and its non-superimposable mirror image that occupy all the sites of a honeycomb lattice. In one range of interactions, we prove that a racemic low-temperature phase occurs (containing equal numbers of each enantiomer). However, in a neighboring range of interactions, we show that a homochiral low-temperature phase (containing a single enantiomer) exists, and thus chiral segregation occurs in the system. Our linear programming technique yields these results in wider ranges of interactions than the m-potential method.     

Studies of intermolecular interactions by matrix isolation vibrational spectroscopy and normal coordinate analysis: Self-association of hydrogen cyanide

A detailed study of the infrared spectra of hydrogen and deuterium cyanide in noble gas, nitrogen and carbon monoxide matrices at 4 K and 20 K has enabled the bands observed to be assigned to monomer, dimer, trimer, tetramer and higher multimer species. Force constants calculated for the linear dimer are used to predict the spectrum of the trimer. The nature of the trapping sites occupied by the monomer and linear dimer, and the structure and trapping site of a second type of dimer observed only in argon matrices, are discussed.     

Super lattice formation of an array of volatile wetting droplets

For an ordered array of critical volatile wetting droplets the formation of a super lattice by an Ostwald-ripening-like competition process is considered. The underlying diffusion problem is treated within a quasistatic approximation and to first order in the inverse droplets distance. The approach is rather general but a square lattice and a triangular lattice are studied explicitly. Dispersion relations for the super lattice growth of these arrays are calculated. Received 29 November 1999 and Received in final form 15 February 2000     

Magnetism of Fe clusters embedded in Cu,Ag, and Au fcc matrices: density functional calculations

We present extensive first principles density functional theory (DFT) calculations dedicated to analyze the magnetic properties of small Fe _n clusters (n = 2,3) embedded in Cu fcc, Ag fcc and Au fcc matrices. We consider several dimers and trimers having different interatomic distances. In all cases the Fe atoms are embedded as substitutional impurities in the metallic network. For the case of the Fe dimers we have considered two magnetic configurations: ferromagnetic (antiferromagnetic), when the atomic magnetic moment of the Fe atoms are parallel (antiparallel) each other. For the case of dimers immersed in Cu and Ag matrices, the ground state corresponds to the ferromagnetic Fe dimer whose interatomic distance is a/√2. For Fe dimer immersed in the Au matrix the ground state corresponds to a ferromagnetic coupling when the interatomic distance is a√(3/2). In the case of the Fe trimers we have considered three or four magnetic configurations, depending on the Fe cluster geometry. For the case of Fe trimer immersed in Cu and Ag matrices we have found that the ground state corresponds to the ferromagnetic trimer forming an equilateral triangle with an interatomic distance equal to a/√2. The ground state for the Fe trimer immersed in the Au matrix corresponds to the ferromagnetic Fe trimer forming a right angle triangle.     

Theoretical study of photoabsorption cross-section of water cluster anions: the size and isomer dependences

Photoabsorption cross-sections of water dimer and trimer anions are calculated with an ab initio molecular orbital method. Because the electron detachment energy of these small water cluster anions is less than 0.3 eV, all of the photoabsorption spectra in the near-infrared and visible region are due to the bound-free transitions. The theoretical spectra of two isomers of dimer anion and three isomers of trimer anion are compared, which suggest the possibility of the identification of the isomer structure by the photoabsorption spectra. The convergence on the basis sets is also examined by adding diffuse functions.     

标定超高压电子显微镜中菊池线的一种有效方法

用电子计算机标定菊池线的困难在于实验误差。误差的来源有二:一是菊池线位置测量的误差;二是仪器常数的误差。本文用最小二乘法拟合菊池线及自动校正仪器常数的办法减少了实验误差,并用点阵平面几何学的方法进行标定,大大地提高了标定的可靠性。本方法具有普遍的适用性,但更适合于超高压电镜中菊池线的标定。 关键词：     

Elementary excitations in the symmetric spin-orbital model

Possible types of elementary excitations in the symmetric spin-orbital model on a square lattice are analyzed using a spherically symmetric self-consistent approach. The excitation spectra are calculated. The behavior of the corresponding correlation functions depending on the temperature and parameters of the model is studied. A schematic phase diagram is plotted. It is shown that the thermodynamics of the system is mainly determined by elementary excitations with the entangled spin and orbital degrees of freedom.