LRO in Lattice Systems of Linear Classical and Quantum Oscillators. Strong Nearest-Neighbor Pair Quadratic Interaction

For systems of one-component interacting oscillators on the d-dimensional lattice, d>1, whose potential energy besides a large nearest-neighbour (n-n) ferromagnetic translation-invariant quadratic term contains small non-nearest-neighbour translation invariant term, an existence of a ferromagnetic long-range order for two valued lattice spins, equal to a sign of oscillator variables, is established for sufficiently large magnitude g of the n-n interaction with the help of the Peierls type contour bound. The Ruelle superstability bound is used for a derivation of the contour bound.     

Study of surface properties of blend films using stereocomplexation between enantiomeric polylactide chains

This study investigated the stereocomplex-induced surface structure of enantiomeric poly(lactide) (PLA) blend films by differential scanning calorimeter, electron spectrometer for chemical analysis, and contact angle measurements. The design of the blend systems is based on principles of surface segregation of a modified component with a low surface energy, fluorocarbons (F), as an end group. The two blend systems, uncomplexed (F-l-PLA/l-PLA) and complexed (F-l-PLA/d-PLA), showed quite different surface structures: the surface segregation of fluorocarbon groups in the (F-l-PLA/l-PLA) blend film was observed while the surface structure of the (F-l-PLA/d-PLA) blend film was similar to its bulk one. This indicates that the interchain interaction to form stereocomplexes between l- and d-PLA is strong enough to overcome the driving force of fluorocarbon groups toward the surface.     

Hypercube stacking: A potts-spin model for surface growth

We present a deposition and evaporation model for surface growth under a solid-on-solid constraint. We generalize the Ising-spin representation of a two-dimensional surface by Blöte and Hilhorst to ad-dimensional surface of a (d+1)-dimensional hypercubic lattice. The allowed surface configurations correspond to the (degenerate) ground states of a chirald-state Potts model. We describe a vectorized multisite-coding implementation for the corresponding kinetic Potts-spin model ford=2 andd=3. For thed=2 equilibrium surface our simulation results show excellent agreement with an exact analysis.     

The Knudsen Ion Layer Problem in the Theory of the Collisionless Sheath

The interaction of a partially ionized continuum gas with a negatively charged electrode is investigated theoretically. It is supposed that l_d ? 1, where l_d is the Debye length, l is the mean-free-path. The self-consistent solution is given for two cases: l_I ? l and l_I ～ l, l_I is the effective ionisation length. The matched asymptotic expansions method is used. The Bohm sheath criterion is shown to be satisfied automatically in the considered cases.     

Modelling capillary filling dynamics using lattice Boltzmann simulations

We investigate the dynamics of capillary filling using two lattice Boltzmann schemes: a liquid-gas model and a binary model. The simulation results are compared to the well-known Washburn's law, which predicts that the filled length of the capillary scales with time as l ∝ t ^1/2. We find that the liquid-gas model does not reproduce Washburn's law due to condensation of the gas phase at the interface, which causes the asymptotic behaviour of the capillary penetration to be faster than t ^1/2. The binary model, on the other hand, captures the correct scaling behaviour when the viscosity ratio between the two phases is sufficiently high.     

Localization for random potentials supported on a subspace

We consider the lattice Schrödinger operator acting onl ² ( ^d ) with random potential (independent, identically distributed random variables), supported on a subspace of dimension 1 v <d. We use the multiscale analyses scheme to prove that this operator exhibits exponential localization at the edges of the spectrum for any disorder or outside the interval [-2d, 2d] for sufficiently high disorder.     

Order parameters forn-vector spin glasses ind dimensions

We report Monte Carlo simulations of the time-dependent behavior of Edwards-Anderson spin glasses with Gaussian nearest-neighbor exchange, for both spin dimensionalityn and space dimensionalityd from 2 up to 6. A (nearly) logarithmic decay of the Edwards-Anderson order parameter with time is observed for alln and alld, similar to earlier studies forn=1. But the Monte Carlo data forn>1 suggest stronger than those forn=1 that all order parameters considered vanish in thermal equilibrium for nonzero temperature, because the decay forn>1 is faster at the temperatures of interest. For Heisenberg spins (n=3) no significant dependence of the Edwards-Anderson order parameterq on the size of the lattice was observed ford=2,3 and 4, whereas ford=5 and 6,q was smaller for smaller systems (in contrast to thed=5 Ising case). These results are the first Monte Carlo indication of a change in the bulk behavior of Heisenberg spin glasses at dimensionalityd=4. Quenching the system to zero temperature and then applying a field we find that the order parameter , measuring the alignment with respect to the state at zero field, is destroyed by a sufficiently strong magnetic field, for all observedn andd.Sonderforschungsbereich 125 Aachen-Jülich-Köln, FRG     

Cluster variation method for lattice models

A noncombinatorial variation method for calculation of thermodynamic and correlation functions in a wide class of lattice models is developed. The method is illustrated on the model of a two-dimensional lattice gas consisting ofM kinds of molecules with pairwise interaction.     

Finite-size scaling in the theory above the upper critical dimension

We derive exact results for several thermodynamic quantities of the O ( n ) symmetric field theory in the limit in a finite d-dimensional hypercubic geometry with periodic boundary conditions. Corresponding results are derived for an O ( n ) symmetric model on a finite d-dimensional lattice with a finite-range interaction. The leading finite-size effects near T_c of the field-theoretic model are compared with those of the lattice model. For 2 < d < 4, the finite-size scaling functions are verified to be universal. For d > 4, significant lattice effects are found. Finite-size scaling in its usual simple form does not hold for d > 4 but remains valid in a generalized form with two reference lengths. The finite-size scaling functions of the field theory turn out to be nonuniversal whereas those of the lattice model are independent of the nonuniversal model parameters. In particular, the field-theoretic model exhibits finite-size effects whose leading exponents differ from those of the lattice model. The widely accepted lowest-mode approach is shown to fail for both the field-theoretic and the lattice model above four dimensions. Received: 20 October 1997 / Accepted: 5 March 1998     

Exact solution of a three-component system on the honeycomb lattice

A model three-component system is considered in which the bonds of a honeycomb lattice are covered by rodlike molecules of typesAA, BB, andAB. The ends of molecules near a common lattice site interact with energies _AA, _BB, and _AB. The model is equivalent to an Ising model on the 3–12 lattice. Exact results are obtained for the two-phase coexistence curves in the isothermal composition plane.     

Zero and finite temperature phase diagram of the spinless fermion model in infinite dimensions

The phase diagram of the model of spinless fermions with repulsive nearest neighbour interaction is calculated analytically on a hypercubic lattice in infinite dimensions (d → ∞). In spite of its simplicity the model displays a rich phase diagram depending on the doping δ, the interaction U and the temperature T. The system can be in the homogeneous phase (HOM), the nonsegregated AB charge density wave (AB-CDW), the AB phase separation region (PS-AB/HOM; coexistence of AB-CDW and HOM), the incommensurate phase (IP) or the IP phase separation region (PS-AB/IP; coexistence of AB-CDW and IP). We identify three important values of the interaction U_IPL = 0.572 < U_IPH = 1.914 < U_IP/PS = 4.212 which distinguish four intervals of U. These imply four different types of phase diagrams. In all the three phase diagrams with U below U_IP/PS the IP appears. We propose a new general ansatz for the order parameter of this phase. A competition between the IP, the PS-AB/IP and the PS-AB/HOM is found. The relevance of our findings for the phase scenario of the Hubbard model is shown.     

Families of commuting transfer matrices and integrable models with disorder

A family of commuting transfer matrices is shown to be associated to each symmetry transformation of a given Yang-Baxter algebra. This applies in lattices models and field theory.The Yang-Baxter algebra remains unchanged when an arbitrary parameter μ_l is associated to each lattice site. We generate in this way integrable one-dimensional hamiltonians with long-range couplings and disorder given by the <{;μ₁<};. These operators are lattice versions of the non-local charges in sigma models. As a simple example we get a Dzialozhinski-Moriya interaction with an arbitrary coupling per site from the six-vertex model. A similar model with a disordered magnetic field follows too. Their exact solution by an algebraic Bethe ansatz is presented. We derive the excitations spectrum in terms of the density of parameters (μ).As another application, the total spin S² is computed for a XXZ Heisenberg chain (μ_l ≡ 0) as a function of the anisotropy Δ (− ∞ < Δ < + ∞).     

Universality in diffusion front growth dynamics

We have studied the scaling properties of diffusion fronts by numerical calculations based on the mean field approach in the context of a lattice gas model, performed in a triangular lattice. We find that the height-height correlation function scales with time t and length l as C(l, t) ≈l ^α f (t/l ^α/β) with α = 0.62±0.01 and β = 0.39±0.02. These exponent values are identical to those characterising the roughness of the diffusion fronts evolving through a square lattice [1,2], thus confirming their universality. Received 14 November 2001 / Received in final form 20 April 2002 Published online 31 July 2002     

Interaction induced localization in a gas of pyramidal molecules

We propose a model to describe a gas of pyramidal molecules interacting via dipole-dipole interactions. The interaction modifies the tunneling properties between the classical equilibrium configurations of the single molecule and, for sufficiently high pressure, the molecules become localized in these classical configurations. We explain quantitatively, without free parameters, the shift to zero frequency of the inversion line observed upon increase of the pressure in a gas of ammonia or deuterated ammonia. For sufficiently high pressures, our model suggests the existence of a super-selection rule for states of different chirality in substituted derivatives.     

Existence of phase transitions for quantum lattice systems

We prove that the following lattice systems:

1. anisotropic Heisenberg model,
2. Ising model with transverse magnetic field,
3. quantum lattice gas with hard cores extending over nearest neighbours,

exhibit phase transitions if the temperature is sufficiently low and the transverse (or kinetic) part of the interaction sufficiently small.     

A mechanism of unexpected temperature dependence of muonic catalysis in solid deuterium

It is shown that, at sufficiently low temperatures, the elastic scattering of dµ mesic atoms (as well as slow neutrons) in solid deuterium proceeds on the whole crystal lattice without energy loss, whereas inelastic scattering with excitation of phonons is weak. For this reason, the resonant formation of ddµ mesic molecules in solid deuterium occurs before the thermalization of dµ mesic atoms, which explains the observed temperature independence of the ddµ-molecule formation rate and muonic catalysis.     

Y型Langmuir-Blodgett膜中分子聚集行为的偶极作用模型

利用经典静电场理论，描述了Y型Langmuir-Blodgett (LB) 膜中棒状分子聚集行为的偶极作用模型，给出了Y型LB膜结构与光谱性质的关系.讨论了Y型膜中分子间距、层间距、分子取向、膜层数等结构参数对分子聚集行为的影响，并在此基础上比较了Y型膜和Z型膜分子聚集行为的异同.理论结果与实验规律符合较好.     

Monte Carlo simulations for two-dimensional quantum systems

The Trotter-Suzuki transformation has been used to obtain the classical representation ford-dimensional lattice systems with boson and fermion degrees of freedom. A Monte Carlo algorithm for the equivalent (d+1)-dimensional classical system is presented. Numerical results are shown for the Heisenberg-spin-glass, the XY model and the spinless fermion lattice gas in two dimensions.     

Determination of Enantiomeric Compositions of Analytes Using Novel Fluorescent Chiral Molecular Micelles and Steady State Fluorescence Measurements

Novel fluorescent chiral molecular micelles (FCMMs) were synthesized, characterized, and employed as chiral selectors for enantiomeric recognition of non-fluorescent chiral molecules using steady state fluorescence spectroscopy. The sensitivity of the fluorescence technique allowed for investigation of low concentrations of chiral selector (3.0 × 10⁻⁵ M) and analyte (5.0 × 10⁻⁶ M) to be used in these studies. The chiral interactions of glucose, tartaric acid, and serine in the presence of FCMMs poly(sodium N-undecanoyl-l-tryptophanate) [poly-l-SUW], poly(sodium N-undecanoyl-l-tyrosinate) [poly-l-SUY], and poly(sodium N-undecanoyl-l-phenylalininate) [poly-SUF] were based on diastereomeric complex formation. Poly-l-SUW had a significant fluorescence emission spectral difference as compared to poly-l-SUY and poly-l-SUF for the enantiomeric recognition of glucose, tartaric acid, and serine. Studies with the hydrophobic molecule α-pinene suggested that poly-l-SUY and poly-l-SUF had better chiral discrimination ability for hydrophobic analytes as compared to hydrophilic analytes. Partial-least-squares regression modeling (PLS-1) was used to correlate changes in the fluorescence emission spectra of poly-l-SUW due to varying enantiomeric compositions of glucose, tartaric acid, and serine for a set of calibration samples. Validation of the calibration regression models was determined by use of a set of independently prepared samples of the same concentration of chiral selector and analyte with varying enantiomeric composition. Prediction ability was evaluated by use of the root-mean-square percent relative error (RMS%RE) and was found to range from 2.04 to 4.06%. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Rigorous Analysis of Discontinuous Phase Transitions via Mean-Field Bounds

 We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice ℤ ^d . Our essential assumption is that these models satisfy the condition of reflection positivity. We prove that whenever the associated mean-field theory predicts a discontinuous transition, the actual model also undergoes a discontinuous transition (which occurs near the mean-field transition temperature), provided the dimension is sufficiently large or the first-order transition in the mean- field model is sufficiently strong. As an application of our general theory, we show that for d sufficiently large, the 3-state Potts ferromagnet on ℤ ^d undergoes a first-order phase transition as the temperature varies. Similar results are established for all q-state Potts models with q≥3, the r-component cubic models with r≥4 and the O(N)-nematic liquid-crystal models with N≥3. Received: 22 July 2002 / Accepted: 12 January 2003 Published online: 5 May 2003 RID="⋆" ID="⋆" ? Copyright rests with the authors. Reproduction of the entire article for non-commercial purposes is permitted without charge. Communicated by J. Z.Imbrie