A mean spherical model with coulomb interactions

We consider simple cubic lattice systems ind dimensions with a continuous real charge variableq(n) at each lattice siten. These variables are subject t'o a mean spherical constraint forcing _n q ²(n)=Q ², where is the number of lattice sites in andQ is an elementary charge. The energy of the charges comes from interactions with an electrostatic potential, which is the solution of a symmetric second-difference Poisson equation on the lattice. Two cases are considered, both of which allow the inclusion of the effects of a fixed, constant, external electric field. On the lattice ₁=[1,N]^d , a Neumann condition is imposed at the surface of the lattice. The lattice ₂=[1,N] [–M,M]^(d–1) is periodic in each direction ranging over [–M, M] and has a Dirichlet condition imposed at the other two surfaces. On ₂ a finite electric field may be applied, while on ₂ a finite potential difference may be applied across the lattice. The models are exactly solvable. We study the distribution functions on each system and show that they satisfy appropriate forms of the first two Stillinger-Lovett moment conditions. The two charge distribution functions show screening behavior at high temperature and extreme short range at an intermediate temperatureT ₀(d), and oscillate as they decay to zero forT<T ₀(d). Because of the continuous nature of the charge variables, there is no Kosterlitz-Thouless transition in two dimensions. In three dimensions the change in the decay behavior of the distribution functions atT<T ₀(d) is precursor to a phase transition to a charge ordered state.     

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T$T$, a quantum parameter g$g$, and the ratio p=−_J2/_J1$p=-J_2/J_1$, where _J1>0$J_1>0$ refers to ferromagnetic interactions between first-neighbour sites along the d$d$ directions of a hypercubic lattice, and _J2<0$J_2<0$ is associated with competing antiferromagnetic interactions between second neighbours along m≤d$m\le d$ directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0$g=0$ space, with a Lifshitz point at p=1/4$p=1/4$, for d>2$d>2$, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0$T=0$ phase diagram, there is a critical border, _gc=_gc(p)$g_c=g_c\left(p\right)$ for d≥2$d\ge 2$, with a singularity at the Lifshitz point if d<(m+4)/2$d<(m+4)/2$. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4$p=1/4$.     

Classical coulomb systems near a plane wall. I

The equilibrium structure of classical Coulomb systems bounded by a plane wall is studied near that wall. Several models are considered: the two-dimensional one-component plasma at a special value of the coupling constant (which makes the model exactly soluble), the two-dimensional and three-dimensional one-component and two-component plasmas in the weak-coupling limit (a Debye-Hückel type of approach is then used). Along a wall, the pair correlation functions decay only as an inverse power of the distancer, namely, asr ^–v for av-dimensional system (v=2,3). The one-body densities are also studied; the first BGY equation is used.     

Analytic solution of the mean spherical approximation for ion-dipole model in a neutralizing background

The analytic solution of the mean spherical approximation (MSA) for a multicomponent mixture of hard ions and hard dipoles with arbitrary valences and sizes of particles in a uniform neutralizing background is found. Expressions for the pair correlation functions and thermodynamics in the MSA are obtained.     

The influence of external boundary conditions on the spherical model of a ferromagnet. I. Magnetization profiles

The spherical model of a ferromagnet is investigated for various (external) boundary conditions. It is shown that, besides the well-known critical point, a second one can be produced by the boundary conditions. Although the main asymptotic of the free energy is analytic at the new critical point, theO(N^1–2/d) asymptotic possesses a singularity here. A natural order parameter of the model has singularities at both critical points. The magnetization profile is studied for the whole range of the model's parameters and at different scales. It is shown that (in an appropriate regime) below the second critical temperature the magnetization profile freezes, that is, becomes temperature independent. Distributions of the single spin variables and some macroscopic observables (including normalized total spin) are studied for the whole temperature range including the critical points.     

Short-time behavior of the kinetic spherical model with long-ranged interactions

The kinetic spherical model with long-ranged interactions and an arbitrary initial order m₀ quenched from a very high temperature to T is solved. In the short-time regime, the bulk order increases with a power law in both the critical and phase-ordering dynamics. To the latter dynamics, a power law for the relative order is found in the intermediate time-regime. The short-time scaling relations of small m₀ are generalized to an arbitrary m₀ and all the time larger than . The characteristic functions for the scaling of m₀ and for are obtained. The crossover between scaling regimes is discussed in detail. Received 17 September 1999     

Charge Correlations in a Coulomb System Along a Plane Wall: A Relation Between Asymptotic Behavior and Dipole Moment

Classical Coulomb systems at equilibrium, bounded by a plane dielectric wall, are studied. A general two-point charge correlation function is considered. Valid for any fixed position of one of the points, a new relation is found between the algebraic tail of the correlation function along the wall and the dipole moment of that function. The relation is tested first in the weak-coupling (Debye–Hückel) limit, and afterwards, for the special case of a plain hard wall, on the exactly solvable two-dimensional two-component plasma at coupling =2, and on the two-dimensional one-component plasma at an arbitrary even integer .     

Fluorescence intensity and anisotropy decays of the intrinsic tryptophan emission of hemoglobin measured with a 10-GHz fluorometer using front-face geometry on a free liquid surface

We measured the intensity and anisotropy decays of the intrinsic tryptophan emission from hemoglobin solutions obtained using a 10-GHz frequency-domain fluorometer and a specially designed cuvette which allows front-face excitation on a free liquid surface. The cuvette eliminates reflections and stray emissions, which become significant for low-intensity fluorescence such as in hemoglobin. Three lifetimes are detectable in the subnanosecond range. The average lifetime of hemoglobin emission is ligand dependent. The measured values of average lifetimes are 91, 174, and 184 ps for deoxy-, oxy-, and carboxyhemoglobin, respectively. Fluorescence anisotropy decays of oxy-, deoxy-, and carbonmonoxyhemoglobin can be fitted with up to three correlation times. When three components are used, the floating initial anisotropyr _o is, in each case, higher than the steady-state anisotropy of tryptophan in vitrified solution. For deoxy hemoglobin it is close to 0.4. The data are consistent with an initial loss of anisotropy from 0.4 to about 0.3 occurring in the first 2 ps.     

A continuum model of a solid with a free surface: II. Considerations of application of the model to particle-surface interaction theory

Considerations of application of a continuum model of a solid with a free surface to particle-surface interaction theory are presented. The work is based on the recent normal-mode analysis of such a model by the author. It is shown that the model has some important unrealistic properties which do not occur in discrete-lattice models, and it is concluded that considerable care is needed in interpreting some of the predictions of the model, particularly with regard to the importance of normal modes of the non-bulk type, for example surface modes.     

Classical Coulomb systems near a plane wall. II

The equilibrium structure of classical Coulomb systems bounded by a plane hard wall is studied near that wall. A general sum rule is derived for the asymptotic form of the charge-charge correlation function along the wall. The exact results which can be obtained for the two-dimensional one-component plasma provide a test for this new sum rule, as well as for other already known sum rules or their generalizations.This laboratory is associated with the Centre National de la Recherche Scientifique.     

A continuum model of a solid with a free surface: I. Normal mode analysis of the model

A complete analysis is made of the normal modes of an isotropic continuum model of a solid which occupies the region (0, 0, 0) < (x, y, z) < (X, Y, Z), the limit (X, Y, Z) → (∞,∞,∞) being taken. The surface z = 0 is a free surface and that z = Z is fixed; cyclic boundary conditions are used in the x and y directions. The modal displacements (vectors), modal frequencies (as a function of the wave-vectors), and wave-vector-densities are obtained for all types of normal modes; the work is a modification and extension of that of earlier workers.     

A diatomic network model for electronic states of bulk,surface and thin films

This paper reports our investigations on an exactly solvable network model of solids. General properties of diatomic lattices, in particular the dispersion relations for the energy levels, the structure of the energy bands and the density of states for bulk, surface and thin films are compared with the corresponding properties of the monatomic lattices which we have previously reported. For a thin film of finite thickness, we present a simple but informative method of analyzing Van Hove singularities in the density of states. Effects due to the inclusion of second neighbor interactions are also studied. Calculations are exact and the method has apparent advantages over other methods of discussing similar problems.     

Spin-spin correlation function in the two-dimensional Ising model with linear defects. II.T>T c

The dispersion expansion for the spin correlation function in the two-dimensional Ising model with linear defects aboveT _c is derived. The asymptotic behavior is computed by a steepest descent analysis. The lattice is divided into four domains with different asymptotic behaviors. In particular, the correlation length inside certain domains is a function of the defect.     

order and disorder lines in systems with competing interactions: II. The IRF model

Systems with competing interactions can be often exactly solved on a restricted subspace of the parameter space, called an order or disorder trajectory. A simple method introduced within the transfer matrix formalism allows for the calculation of the free energy and spin-spin correlation functions along the order and disorder lines of the Ising model with all possible interactions around a face of the square lattice (IRF model). The general eight-vertex model is thoroughly examined and shows full analogy with the quantum spin chain results of the previous paper.On leave from and address after September 1, 1982: Institute for Theoretical Physics, Eötvös University, 1088 Budapest, Puskin U. 5–7, Hungary.     

Application of a multiregion model to the EM scattering from a rough surface with or without a target above it

An efficient multiregion model is introduced to calculate the electromagnetic scattering from a perfectly electrical conducting(PEC) rough surface with or without a PEC target above it.In the multiregion model,the rough surface is split into multiple regions depending on their position along the rough surface.Two intermediate regions are chosen as the dominant region.If a target is located above the rough surface,the target will also be included in the dominant region.The method of moments(MOM) is only adopted on the dominant region to ensure validity.Hence,the new model can greatly reduce the number of unknowns associated with full MOM analysis.The induced electric currents on the other regions are obtained by approximately considering the mutual coupling between different regions along the rough surface.Compared with the published hybrid method,this new model is not only suitable for EM scattering from a target above a rough surface but also applicable for just rough surfaces.Several numerical simulations are presented to show the validity and efficiency of the multiregion model.     

Stability of interfaces in a random environment. A rigorous renormalization group analysis of a hierarchical model

We study a hierarchical model of domain walls in aD-dimensional bond disordered Ising model at low temperatures. Using a renormalization group method inspired by the work of Bricmont and Kupiainen for the random field Ising model, we prove the existence of rigid interfaces at low enough temperatures in dimensionsD>3.     

Remnant Fermi surface in a pseudogap regime of the two-dimensional Hubbard model at finite temperature

A precursor effect on the Fermi surface in the two-dimensional Hubbard model at finite temperatures near the antiferromagnetic instability is studied using three different itinerant approaches: the second order perturbation theory, the paramagnon theory (PT), and the two-particle self-consistent (TPSC) approach. In general, at finite temperature, the Fermi surface of the interacting electron systems is not sharply defined due to the broadening effects of the self-energy. In order to take account of those effects we consider the single-particle spectral function A(, 0) at the Fermi level, to describe the counterpart of the Fermi surface at T = 0. We find that the Fermi surface is destroyed close to the pseudogap regime due to the spin-fluctuation effects in both PT and TPSC approaches. Moreover, the top of the effective valence band is located around = (π/2,π/2) in agreement with earlier investigations on the single-hole motion in the antiferromagnetic background. A crossover behavior from the Fermi-liquid regime to the pseudogap regime is observed in the electron concentration dependence of the spectral function and the self-energy. Received 8 September 2000 and Received in final form 20 December 2000     

The Gamow shell model with realistic interactions: a theoretical framework for ab initio nuclear structure at drip-lines

Ab initio approaches are among the most advanced models to solve the nuclear many-body problem. In particular, the no-core–shell model and many-body perturbation theory have been recently extended to the Gamow shell model framework, where the harmonic oscillator basis is replaced by a basis bearing bound, resonance and scattering states, i.e. the Berggren basis. As continuum coupling is included at basis level and as configuration mixing takes care of inter-nucleon correlations, halo and resonance nuclei can be properly described with the Gamow shell model. The development of the no-core Gamow shell model and the introduction of the $\hat{\bar{Q}}$-box method in the Gamow shell model, as well as their first ab initio applications, will be reviewed in this paper. Peculiarities compared to models using harmonic oscillator bases will be shortly described. The current power and limitations of ab initio Gamow shell model will also be discussed, as well as its potential for future applications.