Decay to equilibrium in random spin systems on a lattice. II

We study the continuous spin systems on ad3-dimensional lattice with random ferromagnetic interactions of finite range. We show that, if the temperature is sufficiently high and the probability of interaction to be large is small enough, the almost sure decay to equilibrium has a subexponential upper bound.     

Poisson Approximations for the Ising Model

A d-dimensional Ising model on a lattice torus is considered. As the size n of the lattice tends to infinity, a Poisson approximation is given for the distribution of the number of copies in the lattice of any given local configuration, provided the magnetic field a = a(n) tends to −∞ and the pair potential b remains fixed. Using the Stein-Chen method, a bound is given for the total variation error in the ferromagnetic case. AMS SUBJECT CLASSIFICATION: 60F05, 82B20.     

On the ferromagnetism of high-spin states

It is established on the basis of the idea of strong interaction within the unit cell that ferromagnetic instability is possible in a system with hopping between d-electron states of atoms that are in high-spin states and form a bcc lattice. The phase diagram of the existence of ferromagnetic ordering as a function of the degree of filling of the d shell is constructed. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 275–280 (25 August 1998)     

Transmission of electrons through ferromagnetic material and applications to detection of electron spin polarization

The salient features of the total low energy inelastic electron scattering cross section in transition metals are described by a constant term σ₀ plus a term σ_d that is proportional to the number of unoccupied d-orbitals. This simple model predicts that low energy electrons transmitted through a ferromagnetic ultrathin film acquire a transport spin polarization a(χ). Using the ratio σ₀/σ_d as the only adjustable parameter, the model predicts the enhancement of the spin polarization of the low energy cascade electrons as well as a(χ) in reasonable agreement with the existing observations on Fe, Co and Ni. A detector for electron spin polarization P based on the spin dependent transmission of electrons through ferromagnetic material is proposed which should be superior to existing P-detectors by 1–2 orders of magnitude.     

Recoilless fraction studies of iron near the Curie temperature

The recoilless fractionf of⁵⁷Fe in iron is determined as a function of temperatureT in the vicinity of the Curie temperatureTc using a source of⁵⁷Co diffused in a foil of 100% enriched⁵⁶Fe. Our results show thatf does not undergo an abrupt change atTc, but that in the ferromagnetic phase |df/dT| is larger than in the non-ferromagnetic phase. This indicates that the ferromagnetic interaction increases the bond between the iron atoms, and thus contributes to the stability of the iron lattice belowTc.     

On the spectrum of the Heisenberg Hamiltonian

The quantum, antiferromagnetic, spin-1/2 Heisenberg Hamiltonian on thed-dimensional cubic lattice ^d is considered for any dimensiond. First the anisotropic case is considered for small transversal coupling and a convergent expansion is given for a family of eigenprojections which is complete in all finite-volume truncations. Then the general case is considered, for which an upper bound to the ground-state energy is given which is optimal for strong enough anisotropy. This bound is expressed through a functional involving the statistical expectation value at finite temperature of a certain correlation function of an Ising model defined on the lattice ^d itself.     

Berezinskii–Kosterlitz–Thouless Order in Two-Dimensional O(2)-Ferrofluid

We study a two-dimensional ferrofluid of hard-core particles with internal degrees of freedom (plane rotators) and O(2)-invariant ferromagnetic spin interaction. By reducing the continuous system to an approximating reference lattice system, a lower bound for the two-spin correlation function is obtained. This bound, together with the Fröhlich–Spencer result about the Berezinskii–Kosterlitz–Thouless transition in the two-dimension lattice system of plane rotators, shows that our model also exhibits the same kind of ordering. Namely for a short-range ferromagnetic interaction the two-spin correlation function does not decay faster than some power of the inverse distance between particles, for small temperatures and high densities of the ferrofluid. For a long-range ferromagnetic interaction the model manifests a non-zero order parameter (magnetization) in this domain, whereas for high temperatures spin correlations decay exponentially.     

Analytic Perturbation Theory for Bound States in the Transfer Matrix Spectrum of Weakly Correlated Lattice Ferromagnetic Spin Systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region (β≪1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter α=〈s ⁴〉−3〈s ²〉²>0, i.e. in the region which we call Gaussian subjugation, where 〈s ^k 〉 denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass −lnβ and a bound state below the two-particle threshold. We develop a β analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in β.     

Spectral Analysis of Weakly Coupled Stochastic Lattice Ginzburg–Landau Models

We consider the relaxation to equilibrium of solutions , t>0, , of stochastic dynamical Langevin equations with white noise and weakly coupled Ginzburg–Landau interactions. Using a Feynman–Kac formula, which relates stochastic expectations to correlation functions of a spatially non-local imaginary time quantum field theory, we obtain results on the joint spectrum of H, , where H is the self-adjoint, positive, generator of the semi-group associated with the dynamics, and P ^j , j= 1, …, d are the self-adjoint generators of the group of lattice spatial translations. We show that the low-lying energy-momentum spectrum consists of an isolated one-particle dispersion curve and, for the mass spectrum (energy-momentum at zero-momentum), besides this isolated one-particle mass, we show, using a Bethe–Salpeter equation, the existence of an isolated two-particle bound state if the coefficient of the quartic term in the polynomial of the Ginzburg–Landau interaction is negative and d= 1, 2; otherwise, there is no two-particle bound state. Asymptotic values for the masses are obtained. Received: 27 September 2000 / Accepted: 16 January 2001     

The Electronic and Magnetic Properties of FCC Iron Clusters in FCC 4D Metals

The electronic and magnetic structures of small FCC iron clusters in FCC Rh, Pd and Ag were calculated using the discrete variational method as a function of cluster size and lattice relaxation. It was found that unrelaxed iron clusters, remain ferromagnetic as the cluster sizes increase, while for relaxed clusters antiferromagnetism develops as the size increases depending on the host metal. For iron in Rh the magnetic structure changes from ferromagnetic to antiferromagnetic for clusters as small as 13 Fe atoms, whereas for Fe in Ag antiferromagnetism is exhibited for clusters of 24 Fe atoms. On the hand, for Fe in Pd the transition from ferromagnetism to antiferromagnetism occurs for clusters as large as 42 Fe atoms. The difference in the magnetic trends of these Fe clusters is related to the electronic properties of the underlying metallic matrix. The local d densities of states, the magnetic moments and hyperfine parameters are calculated in the ferromagnetic and the antiferromagnetic regions. In addition, the average local moment in iron-palladium alloys is calculated and compared to experimental results.     

Flame front tracking in turbulent lean premixed flames using?stereo PIV and time-sequenced planar LIF of OH

This paper describes the simultaneous application of time-sequenced laser-induced fluorescence imaging of OH radicals and stereoscopic particle image velocimetry for measurements of the flame front dynamics in lean and premixed LP turbulent flames. The studied flames could be acoustically driven, to simulate phenomena important in LP combustion technologies. In combination with novel image post processing techniques we show how the data obtained can be used to track the flame front contour in a plane defined by the illuminating laser sheets. We consider effects of chemistry and convective fluid motion on the dynamics of the observed displacements and analyse the influence of turbulence and acoustic forcing on the observed contour velocity, a quantity we term as s _d ^2D. We show that this quantity is a valuable and sensitive indicator of flame turbulence interactions, as (a) it is measurable with existing experimental methodologies, and (b) because computational data, e.g. from large eddy simulations, can be post processed in an identical fashion. s _d ^2D is related (to a two-dimensional projection) of the three-dimensional flame displacement speed s _d , but artifacts due to out of plane convective motion of the flame surface and the uncertainty in the angle of the flame surface normal have to be carefully considered. Monte Carlo simulations were performed to estimate such effects for several distributions of flame front angle distributions, and it is shown conclusively that s _d ^2D is a sensitive indicator of a quantity related to s _d in the flames we study. s _d ^2D was shown to increase linearly both with turbulent intensity and with the amplitude of acousting forcing for the range of conditions studied.     

Magnetic properties of 3d transition metal monolayers on metal substrates

We report results of systematic calculations for magnetic properties of 3d transition metal monolayers on Pd(001) and Ag(001). We find large similarities to interactions of magnetic 3d impurities in the bulk. Therefore the overlayer results are supplemented with results for 3d dimers in Cu, Ag, and Pd. Differences between the two classes of systems are utilized to reveal the interaction within the overlayers and between overlayers and substrates. In virtually all cases we find both ferromagnetic and antiferromagnetic solutions, showing large magnetic moments and similar densities of states. From the trend of the calculations we conclude that V, Cr, and Mn overlayers favor the antiferromagnetic c(2×2) structure, while Ti, Fe, Co, and Ni prefer the ferromagnetic one.     

Temperature phase transitions associated with local minima of energy

We develop an alternative version of the theory of contour models adapted to continuous spins located in sites of a ($d⩾2$)-dimensional lattice. The spins interacting via nearest-neighbor ferromagnetic interactions are embedded in a single spin potential $V$ similar to that already introduced by Dobrushin and Shlosman. The potential $V$ has a finite-ordered sequence of local minima and satisfy certain conditions. For all finite-reciprocal temperatures less than one, we prove the Peierls condition and we show that there exists a sequence of first-order phase transition temperature points.     

Discontinuity of surface tensions in the q-state Potts model

For the ferromagnetic scalar q-state Potts model on a d-dimensional cubic lattice we prove the following results: (1) We derive a correlation inequality and then we prove that the surface tension between two ordered phases exists in dimension d ⩾ 2 whenever q ⩾ 2 and it is discontinuous at the transition point whenever q is large enough. (2) At the limit q↗ ∞ the surface tension between an ordered phase and the disordered one vanishes everywhere except at the transition point.     

Diffraction Spectrum of Lattice Gas Models above T c

The diffraction spectra of lattice gas models on ^d with finite-range ferromagnetic two-body interactions above T _c or with certain rates of decay of the potential are considered. We show that these diffraction spectra almost surely exist, are ^d-periodic and consist of a pure point part and an absolutely continuous part with continuous density.     

Spin fluctuations and peculiarities of semiconductor-metal electronic transitions in almost ferromagnetic compounds of transition metals

The influence of spin fluctuations on the energy spectra of sp and d current carriers in almost ferromagnetic semiconductors based on compounds of d transition metals is examined. It is shown that because electron spectra split in the fluctuating exchange fields in almost ferromagnetic systems, electronic transitions of the type semiconductor-metal are possible, accompanied by the disappearance of energy gaps in the spectra of the sp and d electrons at various temperatures and by a shift of the chemical potential into the region of allowed energies. A specific analysis of similar electronic transitions is presented, based on the almost ferromagnetic compound FeSi. Fiz. Tverd. Tela (St. Petersburg) 41, 1792–1796 (October 1999)     

Wegner-type Bounds for a Two-particle Lattice Model with a Generic “Rough” Quasi-periodic Potential

In this paper, we consider a class of two-particle tight-binding Hamiltonians, describing pairs of interacting quantum particles on the lattice ℤ ^d , d ≥ 1, subject to a common external potential V(x) which we assume quasi-periodic and depending on auxiliary parameters. Such parametric families of ergodic deterministic potentials (“grands ensembles”) have been introduced earlier in Chulaevsky (2007), in the framework of single-particle lattice systems, where it was proved that a non-uniform analog of the Wegner bound holds true for a class of quasi-periodic grands ensembles. Using the approach proposed in Chulaevsky and Suhov (Commun Math Phys 283(2):479–489, 2008), we establish volume-dependent Wegner-type bounds for a class of quasi-periodic two-particle lattice systems with a non-random short-range interaction.     

ab-initio investigations of electronic and magnetic properties of the tetragonal chalcopyrite BeTiTe2 compound: DFT + U study

The spin-polarised structural, electronic, and magnetic properties of the chalcopyrite BeTiTe₂ compound in tetragonal structure (Be_0.50Ti_0.50Te) have been studied by employing first-principles full-potential linearised augmented plane wave plus local orbitals (FP-L/APW?+?lo) method within the density functional theory (DFT) and implemented in WIEN2k code. The exchange and correlation energy are described in two frameworks of GGA (generalised gradient approximation) and GGA?+?U (U is the Hubbard term). The structural analysis confirms that the ferromagnetic phase of the tetragonal BeTiTe₂ compound (Be_0.50Ti_0.50Te) is energetically more favourable; also different equilibrium lattice parameters, such as lattice constants (a₀ and c₀), bulk modulus (B₀), and its first-pressure derivative (B?) have been evaluated in both paramagnetic and ferromagnetic phases. The electronic results of the tetragonal BeTiTe₂ compound show a complete half-metallic behaviour. Moreover, the computed total magnetic moment of this compound is close to 4 μ_B, confirming its half-metallic ferromagnetic nature.     

Paraconductivity for a d-wave superconductor in short-wavelength fluctuation regime

A theoretical study of the fluctuation conductivity above T_c (paraconductivity) is reported for a d-wave superconductor with resonant scattering impurities. A d-wave system is modeled by tight-binding electrons in the two-dimensional squared lattice, and the impurity scattering is treated in the T-matrix approximation in a unitary limit. In calculating the Aslamazov–Larkin (AL) and the Maki–Thompson (MT) terms, we also consider effects of a short-wavelength cutoff in the fluctuation spectrum. The d-wave character in the AL and MT terms manifests itself to renormalization effects on the fluctuation amplitude and reduced temperature, whereas an anomalous-MT term is absent. The present calculations can describe fairly well experiments on the paraconductivity in zinc-doped cuprate superconductors provided that effects of a total-energy cutoff are taken into account.     

Exactly solvable model exhibiting a multicritical point

A hypercubic d-dimensional lattice of spins with nearest neighbor ferromagnetic coupling and next nearest neighbor antiferromagnetic coupling along a single axis is studied in the spherical model limit (n→∞) and is found to exhibit a multicritical point of the uniaxial Lifshitz type. The shape of the λ line is calculated explicitly in the vicinity of the multicritical point, and analytic expressions are given for the shift exponent ψ(d) and its amplitudes A_±(d). The amplitude A_(d) changes sign for d = 3.