Vertical Dimers Research Articles

Non-conserved magnetization operator and ‘fire-and-ice’ ground states in the Ising-Heisenberg diamond chain

We consider the diamond chain with S = 1/2 XYZ vertical dimers which interact with the intermediate sites via the interaction of the Ising type. We also suppose all four spins form the diamond-shaped plaquette to have different g-factors. The non-uniform g-factors within the quantum spin dimer as well as the XY-anisotropy of the exchange interaction lead to the non-conserving magnetization for the chain. We analyze the effects of non-conserving magnetization as well as the effects of the appearance of negative g-factors among the spins from the unit cell. A number of unusual frustrated states for ferromagnetic couplings and g-factors with non-uniform signs are found out. These frustrated states generalize the “half-fire-half-ice” state introduced in reference Yin et al. (2015). The corresponding zero-temperature ground state phase diagrams are presented.

Stationary measure of the driven two-dimensional $q$-Whittaker particle system on the torus

We consider a q-deformed version of the uniform Gibbs measure on dimers on the periodized hexagonal lattice (equivalently, on interlacing particle configurations, if vertical dimers are seen as particles) and show that it is invariant under a certain irreversible q-Whittaker dynamic. Thereby we provide a new non-trivial example of driven interacting two-dimensional particle system, or of (2+1)-dimensional stochastic growth model, with explicit stationary measure. We emphasize that this measure is far from being a product Bernoulli measure. These Gibbs measures and dynamics both arose earlier in the theory of Macdonald processes. The q=0 degeneration of the Gibbs measures reduce to the usual uniform dimer measures with given tilt, the degeneration of the dynamics originate in the study of Schur processes and the degeneration of the results contained herein were recently treated in work of the second author.

A Cluster Expansion Approach to the Heilmann–Lieb Liquid Crystal Model

A monomer-dimer model with a short-range attractive interaction favoring colinear dimers is considered on the lattice $\mathbb{Z}^2$. Although our choice of the chemical potentials results in more horizontal than vertical dimers, the horizontal dimers have no long-range traslational order - in agreement with the Heilmann-Lieb conjecture.

Plasmonicverticaldimer arrays as elements for biosensing.

Localized surfaceplasmon resonances of metallic nanoparticles can be used for biosensing because of their sensitive dependence on the refractive index of the surrounding medium. The binding of molecules to the particles causes a change of the effective refractive index in their close vicinity, which leads to a reversible shift of the resonance. We present simulations and sensing experiments of a plasmonresonancebased biosensor that makes use of the narrow antisymmetric resonance in coupled plasmonic vertical dimers. The sensitivity of the antisymmetric resonance is compared with that of a surface lattice resonance for refractiveindex sensing of bulk and of thin layers of molecules. The functionality of such a sensor surface is demonstrated via a testosterone immunoassay for detection of antibody from a solution by binding to surface-immobilized antigen in a fluidic channel.

A [formula omitted]-matrix existence theorem and equivalent tiling problems with dimers and monomers

Let R=(r1,r2,…,rm) and S=(s1,s2,…,sn) be nonnegative integral vectors. The class A1(R,S) of (0,1)-matrices with row sum vector R, column sum vector S, and no two consecutive 1's in any column is introduced. Matrices in this class correspond to certain tilings of rectangles by vertical dimers and monomers and arise in the inverse eigenvalue problem for graphs. The main theorem gives necessary and sufficient conditions for the class A1(R,S) to be nonempty. The conditions can be expressed as a system of majorizations in the spirit of the Gale–Ryser theorem. The class A1(R,S) is associated with a type of interchange graph, which is proved to be connected. Also, in the case when A1(R,S) contains a single matrix, the structure of this matrix is identified.

Plasmonics properties of nano-torus: An FEM method

Nano-torus particles are promising in nano-photonics applications. In this paper, we investigate the plasmonics resonant spectrum of torus and the corresponding horizontal and vertical dimers with the finite element method (FEM) based on strict electromagnetic theory. Compared with sphere, single torus and horizontal dimer under perpendicular polarization are characterized with narrower line width and wider tunability throughout visible and infrared frequencies. These properties make single torus and horizontal dimer suitable for high sensitivity sensing. Furthermore, Purcell factor and local field enhancement of horizontal dimer which are important to high efficient single photon devices are one order of magnitude higher than those of single torus respectively. However, vertical dimer under perpendicular polarization has no above advanced characteristics.

Structural studies of decavanadate compounds with organic molecules and inorganic ions in their crystal packing

The formation of decavanadates containing amine counter-ions is explored to get a better insight into the resulting crystal packing. From mixtures containing the Schiff base H 2(SO 3-sal) 2en and vanadate, two different compounds containing decavanadate units have been characterised by X-ray diffraction. The structure of 1 consists of [V 10O 28] 6− monomers united by K +, ethylenediamine cations and H 2O molecules, which act as bridging atoms between the layers, forming a three-dimensional array. The structure of 2 contains vanadium triprotonated decavanadate anions, [H 3V 10O 28] 3−, in one-dimensional vertical chains, bonded by interdecavanadate hydrogen bonds. The interchain region is populated by (H 2en) 2+ cations and H 2O molecules, which form a network of hydrogen bonds. From the filtrate solution of the reaction mixture containing V IVOSO 4, d, l-diaminopropionic acid and salicylaldehyde, which also contained triethylamine, a diprotonated decavanadate 3 was obtained. Compound 3 consists of decavanadate vertical dimers, surrounded by triethylamonium cations that preclude the interaction between the dimers. Bond valence calculations were used to confirm the degree of protonation of the decavanadate anions.

Finite-size effects in a dimer model of crystallization

A dimer model of two-dimensional crystallization in melts and solutions with strong interparticle correlations is proposed. The crystal phase is represented by a region of regularly packed vertical dimers growing from a selected layer in which the occupied and vacant vertical bonds alternate. The crystal growth may be stimulated by an “external staggered field” acting on the bonds in the selected layer. The difference of the average occupation numbers of odd and even bonds plays the role of an ordering parameter. In cases when the dimer ordering in the selected layer is imperfect, a coexistence of crystal domains with an orientationally disordered fluid phase takes place. For simplicity the lattice is taken in the form of an infinite cylinder and the dependence of the ordering parameter on the bond activities and finite-size effects with respect to one lattice dimension are studied rigorously. It is found that the ordering parameter vanishes in the thermodynamic limit for arbitrary finite values of the ordering field. The leading-order finite-size correction to the ordering parameter falls off with the increase of the finite lattice dimension L as L −1 for large L.

Nematic ordering in monomer-dimer system with attractive interactions on a square lattice

A monomer-dimer system with excluded volume interactions and weak long range attractive interactions is studied on a two dimensional square lattice. The anisotropic version of the exact series expansion method of Nagle-Temperley has been used to obtain the entropy as a function of densities of horizontal and vertical dimers. Both isotropic and anisotropic long range dispersion interactions are taken into account in an approximation of the mean field type. Numerical analysis of the system yields three types of phase diagrams depending on the ratio R = ωa/ωi of the parameters specifying the strengths of anisotropic ωa and isotropic ωi interactions. For small values of R (type I) the nematic-isotropic phase transition is second order while for larger R (type II and III) a tricritical point appears below which the phase transition is first order. If R is large enough (type III) the vapour pressure curve remains entirely in the nematic stability region. There is no crystallization in this model. Lines of class...

Statistical Mechanics of Dimers on a Plane Lattice

This paper considers the statistical mechanics of hard rigid dimers distributed on a lattice (each dimer occupying two nearest neighbor lattice sites). The problem is solved in exact closed form for a finite $m\ifmmode\times\else\texttimes\fi{}n$ plane square lattice with edges which is completely filled with $\frac{1}{2}\mathrm{mn}$ dimers (close-packed limit). In terms of the activities $x$ and $y$ of horizontal and vertical dimers, the configurational partition function ${Z}_{\mathrm{mn}}(x, y)$ is given in the limit of a large lattice by $limit of\text{}{(\mathrm{mn})}^{\ensuremath{-}1}\mathrm{ln}{Z}_{\mathrm{mn}}(x, y)\text{as}m,n\ensuremath{\rightarrow}\ensuremath{\infty}=\frac{1}{2}\mathrm{ln}y+(\frac{1}{\ensuremath{\pi}})\ensuremath{\int}{0}^{\frac{x}{y}}(\frac{1}{v})invtanv\mathrm{dv}.$ It follows that the free energy and entropy of the system are smooth continuous functions of the densities of horizontal and vertical dimers. The number of ways of filling the lattice with dimers is calculated exactly for $m=n=8$ and is given asymptotically by ${[\mathrm{exp}(\frac{2G}{\ensuremath{\pi}})]}^{\frac{1}{2}\mathrm{mn}}={(1.791623)}^{\frac{1}{2}\mathrm{mn}}$. The results are derived with the aid of operator techniques which reduce the partition function to a Pfaffian and hence to a determinant. Some results are also presented for the more general case with monomers present.