Boundary effects on static spin correlation functions in the isotropicX—Y chain at zero temperature

In this work the static spin correlation of an isotropicX—Y-chain with free ends at zero temperature is dealt with. Following the method of Lieb, Schultz, Mattis the problem is reduced to the evaluation of a determinant of the Cauchy type. With regard to the transverse correlation function we find a change from aR ^–3/4 to aR ^–1/2 behavior if the correlated spins move away from the boundary at fixed mutual distanceR.     

Critical exponents for the long-range Ising chain using a transfer matrix approach

The critical behavior of the Ising chain with long-range ferromagnetic interactions decaying with distance r^α, 1<α<2, is investigated using a numerically efficient transfer matrix (TM) method. Finite size approximations to the infinite chain are considered, in which both the number of spins and the number of interaction constants can be independently increased. Systems with interactions between spins up to 18 sites apart and up to 2500 spins in the chain are considered. We obtain data for the critical exponents ν associated with the correlation length based on the Finite Range Scaling (FRS) hypothesis. FRS expressions require the evaluation of derivatives of the thermodynamical properties, which are calculated with the help of analytical recurrence expressions obtained within the TM framework. The Van den Broeck extrapolation procedure is applied in order to estimate the convergence of the exponents. The TM procedure reduces the dimension of the matrices and circumvents several numerical matrix operations.     

Molecular dynamics study of a classical two-dimensional electron system: positional and orientational orders

Molecular dynamics simulation is used to investigate the crystallization of a classical two-dimensional electron system, in which electrons interact with the Coulomb repulsion. From the positional and the orientational correlation functions, we have found an indication that the solid phase has a quasi-long-range (power-law correlated) positional order and a long-range orientational order. This implies that the long-range 1/r system shares the absence of the true long-range crystalline order at finite temperatures with short-range ones to which Mermin's theorem applies. We also discuss the existence of the “hexatic” phase predicted by the Kosterlitz–Thouless–Halperin–Nelson–Young theory.     

Phonon-assisted spin diffusion in solids

The spin flip-flop transition rate is calculated for the case of spectral spin diffusion within a system of dipolarly coupled spins in a solid where the lattice vibrations are present. Long-wavelength acoustic phonons time-modulate the interspin distance r_ij and enhance the transition rate via the change of the 1/r³_ij term in the coupling dipolar Hamiltonian. The phonon-assisted spin diffusion rate is calculated by the golden rule in the Debye approximation of the phonon density of states. The coupling of the spins to the phonons introduces temperature dependence into the transition rate, in contrast to the spin diffusion in a rigid lattice, where the rate is temperature-independent. The direct (one-phonon absorption or emission) processes introduce a linear temperature dependence into the rate at temperatures not too close to T = 0. Two-phonon processes introduce a more complicated temperature dependence that again becomes simple analytical for temperatures higher than the Debye temperature, where the rate is proportional to T², and in the limit T → 0, where the rate varies as T⁷. Raman processes (one-phonon absorption and another phonon emission) dominate by far the phonon-assisted spin flip-flop transitions.     

C Chemical Shift and C–N Dipolar Coupling Tensors Determined by C Rotary Resonance Solid-State NMR

This work explores the utility of simple rotary resonance experiments for the determination of the magnitude and orientation of ¹³C chemical shift tensors relative to one or more ¹³C–¹⁴N internuclear axes from ¹³C magic-angle-spinning NMR experiments. The experiment relies on simultaneous recoupling of the anisotropic ¹³C chemical shift and ¹³C–¹⁴N dipole–dipole coupling interactions using 2D rotary resonance NMR with RF irradiation on the ¹³C spins only. The method is demonstrated by experiments and numerical simulations for the ¹³C^α spins in powder samples of -alanine and glycine with ¹³C in natural abundance. To investigate the potential of the experiment for determination of relative/absolute tensor orientations and backbone dihedral angles in peptides, the influence from long-range dipolar coupling to sequential ¹⁴N spins in a peptide chain (¹⁴N_i–¹³C^α_i–¹⁴N_i+1 and ¹⁴N_i+1–¹³C′_i–¹⁴N_i three-spin systems) as well as residual quadrupolar–dipolar coupling cross-terms is analyzed numerically.     

Heisenberg-Dirac-van Vleck vector model for a 1D antiferromagnetic chain of localized spins <Emphasis Type="Italic">S</Emphasis> = 1

Magnetic properties of anisotropic crystals with localized spins S = 1 are investigated; for these crystals, the Hamiltonian is derived in the Heisenberg-Dirac-van Vleck form, which includes biquadratic contributions apart from bilinear terms. The ground-state energy of the antiferromagnetic chain of spins S = 1 is calculated in the model of nearest neighbors, and the interaction constant is renormalized using the renorm group method in the case of coarsening of the system. The temperature criterion for the formation of long-range order in the system is obtained. The excitations of this chain in the linear approximation have a dispersion relation differing from that for antiferromagnets with spin S = 1/2 and are separated by an energy gap from the ground state. Allowance for nonlinear contribution leads to the formation of a solitary wave in the form of a dark-bright soliton.     

The discrete Gaussian chain with 1/r n interactions: Exact results

We show that the discrete Gaussian chain with interactionV(r) = 1/(r ²–1/4) is self-dual. At the dual temperaturek _B T = 1 we calculate the height-height correlation function and find that the system is rough. A duality relation is established for the temperature-dependent correlation function exponent. We also consider interactionsV(r)–1/r ⁿ and show that absence of a phase transition for 2 <n < 3 implies absence of a phase transition for 1 <n < 2. All these results have their counterparts in a linear system of charges interacting through a potential which is asymptotically logarithmic (forn = 2) or power-law-like (forn 2.On leave of absence from Chemistry Laboratory III, Universitetsparken 5, 2100 ©, Copenhagen, Denmark.     

Equilibrium concentration of point defects in crystalline4He at O K

We calculate the concentrations of vacancies and intersitials in the ground state of a Bose solid which models⁴He. Because ground-state boson wave functions are nodeless, their probability densities correspond to classical Boltzmann factors, and properties of Bose solids, such as the concentration of vacancies and interstitials, can be calculated using classical statistical mechanics. We model the ground-state wave function of⁴He with the product (Jastrow) form that corresponds to a classical 1/r ^b pair potential, and use a quasiharmonic approximation to calculate the concentrations of vacancies and interstitials in an fcc lattice with this potential. We find that the fractional concentration of vacancies at the melting point is 1.60×10^–5 for 1/r ⁹ and 6.36×10^–6 for 1/r ⁶, while the interstitial fractional concentrations are 1.32×10^–3 and 1.08×10^–5, respectively; the defect concentrations decrease by 7–16 orders of magnitude when the crystal density increases by 50%. At the same density, and with the same 1/r ⁹ potential, the concentration of vacancies in an hcp lattice is essentially the same as in an fcc lattice, but the interstitial concentration is much lower, apparently because the fcc lattice contains a more favorable split-interstitial site than does hcp. Therefore, our fcc vacancy results should be directly relevant for (hcp)⁴He, providing what we think is a lower bound on the vacancy concentration, while the interstitial concentration in⁴He is probably much lower than our results.     

Nuclear magnetic resonance spectra of deuterated methanes and 2,2-dimethylpropane in nematic liquid crystals

A simple variational approach is used to study the expectation values <r ₁₂ ^-1> and <r ₁₂ ²> for the two-electron 1s2p ¹ P and 1s2p ³ P. Several ‘anomalous’ phenomena are clearly displayed by the results, which provide some grounds for criticism of traditional arguments concerning spatial correlation between parallel spins.     

Spectral density method in quantum nonextensive thermostatistics and magnetic systems with long-range interactions

Motived by the necessity of explicit and reliable calculations, as a valid contribution to clarify the effectiveness and, possibly, the limits of the Tsallis thermostatistics, we formulate the Two-Time Green Functions Method in nonextensive quantum statistical mechanics within the optimal Lagrange multiplier framework, focusing on the basic ingredients of the related Spectral Density Method (SDM). Besides, to show how the SDM works, we have performed, to the lowest order of approximation, explicit calculations of the low-temperature properties for a quantum d-dimensional spin-1/2 Heisenberg ferromagnet with long-range interactions decaying as 1/r^p ( r is the distance between spins in the lattice).     

Dependence of the Amplification of Giant Raman Scattering and Fluorescence on the Distance between an Adsorbed Molecule and a Metal Surface

We have studied the effect of the long-range amplification of secondary radiation of the molecules of oxazine 1 adsorbed on the surface of thin silver film covered by 1–7 Langmuir monolayers of stearic acid. We show that the intensity of the giant Raman scattering (GRS) changes proportionally to r ^–1 with removal of a molecule from the surface of a metal, which is in good agreement with the theory. The distances over which the strength of the electric field enhanced by the surface makes a substantial contribution to the processes mentioned are of the order of 10 nm.     

On the decay of correlations inSO(n)-symmetric ferromagnets

We prove that for low temperaturesT the spin-spin correlation function of the two-dimensional classicalSO(n)-symmetric Ising ferromagnet decays faster than |x|^–constT providedn2. We also discuss a nearest neighbor continuous spin model, with spins restricted to a finite interval, where we show that the spin-spin correlation function decays exponentially in any number of dimensions.Work supported in part by NSF, Grant PHY76-17191A Sloan Fellow     

On the CP topological sigma model and the Toda lattice hierarchy

We propose, in bihamiltonian formalism, a version of the Toda lattice hierarchy that is satisfied by the two point correlation functions of the CP¹ topological sigma model at genus one approximation, and we also show that this bihamiltonian hierarchy is compatible with the Virasoro constraints of Eguchi–Hori–Xiong up to genus two approximation.     

On the magnetic ordering implemented by the s–d exchange interaction

The RKKY perturbation scheme for the spin s–d exchange model is reexamined in the case of a finite number of electrons per impurity. The distribution of impurities is assumed to be random. The free electron gas representing the unperturbed system in the RKKY approach is replaced by a mean-field system h_r asymptotically equivalent to the reduced s–d model H_r which includes part of the s–d exchange. Below the transition temperature T_c of h_r the lowest energy levels of the s–d exchange Hamiltonian H_K resulting from second-order perturbation theory prove to be ordered in the same manner as those of h_r in the limit of weak s–d exchange, favouring the same definite parallel alignment of any pair of impurity spins. It follows therefore that in the low temperature, weak coupling regime, the s–d model exhibits ferromagnetic ordering of impurities. At temperatures above T_c there is no ordering and impurity–impurity exchange has the RKKY form. These observations are consistent with the presence of a low-temperature ferromagnetic phase in numerous compounds with s–d exchange interaction.     

Absence of continuous symmetry breaking in a one-dimensional n−2 model

For a one-dimensional array ofS ^N–1 spins (N 2) with isotropic pair interactions (and more general systems) with J(j–i) obeying sup_n[n^–1 ₁ ⁿ j ²|J(j)|]<, we prove that every equilibrium state is invariant under the natural action ofSO(N). In particular, there is no long-range order of the conventional type. Included is the caseJ(n)=n ^–2.Research partially supported by U.S.N.S.F. Grant No. MCS-78-01885.S. Fairchild Scholar at Caltech. On leave from Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey 08544.     

Characterization of a a-Si:H thin-film transistors and the effect of thermal annealing

An analysis of characteristics of a-Si:H thin-film transistors were performed. The mobility of electrons in the accumulation layer induced by a gate voltage was in a order of 0.5 cm²/V · s at a field strength lower than 1×10⁴V/cm, and proportional toE ^–r at higher electric field, wherer was 0–0.2.The effect of thermal annealing at the temperatures 100–160°C on the parametersV _T andr are discussed. The activation energies for the variation of both parameters were 0.31 eV and 0.33 eV, respectively, that suggests the mechanism influencing both parameters may be the same. The mechanism is discussed in relation to the carrier hopping through the network of localized states.     

Freezing of nonequilibrium domain structures in a kinetic Ising model

We study the freezing of a disordered spin structure upon continuous cooling to absolute zero for a kinetic Ising spin chain with alternating weak and strong bonds. The kinetic equation for the spin pair correlation function is solved analytically in a continuum approximation. The exponent for the asymptotic dependence of the frozen kink density on a characteristic cooling time is found to bez ^–1, wherez is the equilibrium dynamic critical exponent, for a universality class including power-law and exponential cooling, and 1/2 for a logarithmic cooling program which exhibits threshold behavior.     

Long-wavelength behavior of the optimal HNC/O solution for the ground-state of homogeneous liquid4He atT=0 K

The long-wavelength behavior of the two-body correlation factor,u(k), of the ground-state wave function for an homogeneous liquid⁴He at zero temperature is studied. The solutions are obtained from a paired-phonon-analysis within the HNC/O approximation. The cut-off for the phonons is investigated analyzingu(k) at small momenta. It is shown that the numerical results: (a) rule out a pure gaussian cut-off and (b) are in good agreement with the exponential cut-off suggested by Chester and Reatto. The first-sound velocityc ₁ and the cut-off momentumk _c are determined at several densities in the range 0.016–0.025 Å^–3. In addition, a parametrization of these quantities as a function of the density is provided.