A long-range ferromagnetic spin model with periodic boundary conditions

A possible way to study long-range interacting particles in finite–infinite periodic systems is applied to a modified Ising model with ferromagnetic interaction that decays as a 1/r^α law. We verify, by Monte Carlo heat-bath simulations for cases in D dimensions, that the thermodynamic quantities scale in a way proposed by Tsallis, and that the mean field theory is exact in the last model for all 0⩽α⩽D/2 suggested previously by other authors.     

Indirect interaction of Mössbauer nuclei

An expression is deduced for the operator of the indirect interaction of nuclei via the electromagnetic field. The properties of Mössbauer nuclei are described within the pseudospin formalism, which is usually used in the theory of optical two-level systems. The indirect interaction of pseudospins is derived by a method adopted from the theory of superconductivity. It is found that the potentials of this interaction involve terms decreasing as r ^?3, r ^?2, and r ^?1. The estimates demonstrate that the two-particle interaction can contribute significantly to the width of the resonance line, for example, in crystals whose cells contain thulium nuclei.     

On the solid-like phase transition in crystals of polystyrene spheres in aqueous suspensions

We present results of calculations for the fractional energy difference between the bcc and fcc phases present in ordered systems of polystyrene spheres in aqueous suspensions. The theoretical model developed for those systems is an extension of the concept of a Wigner lattice. The interaction between the particles is assumed to be a screened coulomb potential. We conclude that the phase transition occurs when λr₅ = 1.05 where λ^-1 is the Debye screening length and r_s is the radius of the spherical volume of the unitary cell.     

Quantum critical behavior of clean itinerant ferromagnets

We consider the quantum ferromagnetic transition at zero temperature in clean itinerant electron systems. We find that the Landau-Ginzburg-Wilson order parameter field theory breaks down since the electron-electron interaction leads to singular coupling constants in the Landau- Ginzburg-Wilson functional. These couplings generate an effective long-range interaction between the spin or order parameter fluctuations of the form 1 <r ² d?1, with d the spatial dimension. This leads to unusual scaling behavior at the quantum critical point in 1 < d ≤ 3, which we determine exactly. We also discuss the quantum-to-classical crossover at small but finite temperatures, which is characterized by the appearance of multiple temperature scales. A comparison with recent results on disordered itinerant ferromagnets is given.     

A relativistic Hartree-Fock model for quark systems

The “relativistic H—F” scheme is applied to baryons and finite multiquark sustems. A two-body confinement potential (r, r² or r³) and the one-gluon-exchange interaction are incorporated. The electric OGE term is treated consistently in all considered systems. With the electric OGE term included, the solutions indicate the little bag. (Os)-closed multiquark states, strange or non-strange, cannot be lower in energy than an aggregate of Δ or Λ.     

Thermodynamics and dynamics of systems with long-range interactions

We review simple aspects of the thermodynamic and dynamical properties of systems with long-range pairwise interactions (LRI), which decay as 1/r^d+σ at large distances r in d dimensions. Two broad classes of such systems are discussed. (i) Systems with a slow decay of the interactions, termed “strong” LRI, where the energy is super-extensive. These systems are characterized by unusual properties such as inequivalence of ensembles, negative specific heat, slow decay of correlations, anomalous diffusion and ergodicity breaking. (ii) Systems with faster decay of the interaction potential, where the energy is additive, thus resulting in less dramatic effects. These interactions affect the thermodynamic behavior of systems near phase transitions, where long-range correlations are naturally present. Long-range correlations are often present in systems driven out of equilibrium when the dynamics involves conserved quantities. Steady state properties of driven systems with local dynamics are considered within the framework outlined above.     

Multicomponent dense electron gas as a model of Si MOSFET

We solve a 2D model of N-component dense electron gas in the limit N→∞ and in the range of the Coulomb interaction parameter N ^?3/2?r _s ?1. The quasiparticle interaction on the Fermi circle vanishes as ?²/Nm. The ground-state energy and the effective mass are found as series in powers of r _s ^2/3 . In the quantum Hall state on the lowest Landau level at integer filling 1?ν<N, the charge-activation-energy gap and the exchange constant are Δ=log(r _s N^3/2)?ω_H/ν and J=0.66?ω_H/ν.     

Electron paramagnetic resonance linewidth in a two-dimensional Heisenberg antiferromagnet (S=1/2) with skyrmeons

Electron magnetic relaxation was studied in a two-dimensional Heisenberg antiferromagnet (S=1/2) with skyrmeons. The electron paramagnetic resonance (EPR) linewidth (Г_⊥) was calculated at temperatures T≤J (J is the nearest-neighbor interaction constant). The magnitude of Г_⊥ caused by the Dzyaloshinskii-Moriya interaction is shown to grow as r ₀/a with decreasing temperature, whereas the anisotropic symmetric interaction leads to the (r ₀/a)³ dependence, where r ₀ is the average size of a skyrmeon and a is the lattice parameter. The results obtained agree qualitatively with calculations performed on the basis of a renormalization-group (RG) analysis of the nonlinear σ model at .     

Schrödinger vs. dirac bound state spectra of Q\bar Q-systems and a plausible lorentz structure of the effective power-law potential-systems and a plausible lorentz structure of the effective power-law potential

It is shown that a non-relativistic power-law potential model for the heavy quarks in the form V(r)=Ar ^v+V ₀, (A, ν>0) acquires relativistic consistency in generating Dirac bound states of \(Q\bar Q\) -system in agreement with the Schrödinger spectroscopy if the interaction is modelled by equally mixed scalar and vector parts as suggested by the phenomenology of fine-hyperfine splittings of heavy quarkonium systems in a non-relativistic perturbative approach.     

Renormalization of singular potentials and power counting

We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r² potential perturbed by a 1/r⁴ correction. The power-counting rule, an important ingredient of effective theory, is established by seeking the minimum set of short-range counterterms that renormalize the scattering amplitude. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis.     

Long-range potentials and the electromagnetic polarizabilities

The long-range spin and velocity independent forces of electromagnetic origin which act between any two systems are studied for those cases in which no forces of this type exist to order e². It is shown that they are uniquely determined by the charge, magnetic moment, and polarizabilities of both systems, not only to the dominant order r^?n, but also to the next one r^?(n+1). These potentials provide the link between Compton scattering polarizabilities (response to real photons) and classically defined polarizabilities (response to static electromagnetic field). The two definitions are shown to be equivalent for neutral spinless systems; the problems arising for a neutral particle with magnetic moment are studied in detail. The r^?(n+1) terms have no classical counterpart, since they are due to the relativistic quantum propagation of the system which carries charge or magnetic moment. The results are of general validity with analyticity, crossing, unitarity, and gauge invariance as only inputs. The most general conclusion is that the polarizabilities represent electromagnetic properties of a system at order e², as the charge and magnetic moment do at order e. Thus they give the strength of the response to electric and magnetic fields, independently of the specific characteristics of the electromagnetic agent.     

Analysis of scattering and reactions of aligned7Li-nuclei in a double folding model

Previously measured angular distributions of the differential cross section and the tensor analyzing powerT ₂₀ for the scattering of⁷Li from⁵¹V in the energy range from 10 to 18 MeV were analyzed with the double folding model using the effective nucleon-nucleon interaction M3Y as well as a zero range effective nucleon-nucleon interaction. Due to the spectroscopic deformation of the⁷Li-nucleus the interaction potential contains a central and aT _R -tensor part. The latter one is the origin of the observed tensor analyzing powers. Within the same model the scattering of aligned⁷Li-nuclei from⁵⁸Ni at 14.2 and 20.3 MeV is well described. The strength of theT _R -tensor potential in relation to the spectroscopic mass deformation of⁷Li is discussed. Using the real interaction potential obtained by the double folding model the energy dependence of the total reaction cross sectionσ ^r and its tensor analyzing powerT ₂₀ ^r for the system⁷Li?⁵¹V is well described within a barrier penetration model.     

On the negative point spectrum of quantum mechanical three-body systems

We consider quantum mechanical three-body systems interacting with two-body potentials that are sufficiently regular locally, decrease faster than r^?(2+?) at infinity, and are such that either one two-body subsystem (at least) has a negative energy bound state, or no two-body subsystem has a zero energy bound state or resonance. (This assumption excludes the possibility of the Efimov effect.) We then prove that (1) the discrete spectrum is finite, (2) the point spectrum has no negative accumulation points. (These results have been proved earlier by Sigal and Yafaev, respectively, by different methods and with slightly different assumptions.)     

Two-dimensional electron fluid at high temperature

The two-dimensional and one-component plasma (OCP) model withr ^?1 interactions is investigated in the high-temperature limit, where the thermal wavelength gets larger than the classical distance of closest approach. Nonnegligible diffraction effects are rigorously taken care of (up toe ²) through a temperature-dependent effective interaction. Debye thermodynamics, analyzed in terms of a classical plasma parameter Λ, is shown to diverge as Λ Inh, whenh→0. There is no classical limit. A result at variance with the corresponding one in three dimensions.     

Approach to saturation of the magnetization of dilute AuFe alloys

We present a reinterpretation of our recent measurements of the magnetic properties of some dilute AuFe alloys. We find that the observed approach to saturation of the magnetization for these AuFe alloys can be understood if both single-impurity (Kondo) effects and effects due to interactions between impurities via the Rudeman-Kittel-Kasuya-Yosida (RKKY) interaction, V(r) = (V₀ cos 2k_Fr)/r³, are properly included in the analysis. The analysis yields for the strength of the RKKY interaction V₀ = (1.1 ± 0.3) × 10^-36ergcm³, for the s-d exchange parameter |J| = (1.9 ± 0.3) eV, and for the Kondo temperature T_K = (0.8 ± 0.1) K. We conclude that mean free path effects do not significantly influence the observed approach to saturation of the magnetization for the AuFe alloys studied.     

Legendre transforms and r-particle irreducibility in quantum field theory: The formal power series framework

We study the higher Legendre transforms Γ^(r) {A } of the generating functional G for connected Green's functions in Euclidean boson field theories. To analyze Γ^(r) {A } rigorously even when it does not make sense as an ordinary functional, we develop the framework of formal power series in A. For r = 1, 2 we isolate regularity conditions on G that ensure the existence of Γ^(r) as a formal power series and we verify these conditions for the weakly coupled P(φ)₂ model. We also establish the improved regularity of the functional Φ^(r) obtained by subtracting from Γ^(r) its trivial singular part.     

Long Range Potential Component in the NN Force

The Fourier transform of the Born term of the AGS equation in the NNπ-system generates an energy-dependent Yukawa-type local NN-quasi-potential. An appropriate average with respect to energy suggests a variety of local NN-potentials with different ranges: 1/r(r + a) ^m?1 (for 2 ≤ m) where in the long range region it becomes 1/r ^m , while in the short range region the Yukawa-type potential e ^?(m?1)r/a /r results. Therefore, one finds that the Yukawa potential is automatically accompanied by an additional longer range interaction 1/r ^m . For m = 2, the potential 1/r ² produces Efimov-like bound states in the deuteron spectra. The m = 6, 7 cases lead to the Van der Waals potential.     

Screening of excitonic states by low-density 2D charge carriers in GaAs/AlGaAs quantum wells

Screening of excitonic states by a system of 2D electrons (or holes) in GaAs/AlGaAs single quantum wells is studied. With increasing concentration of 2D charge carriers, a threshold-type disappearance of excitonic states is observed in both luminescence and reflectance spectra. The higher the quality of the 2D system, the lower the corresponding threshold concentration. In the best systems, the collapse of excitonic states occurs at unexpectedly low electron densities n _e =5×10⁹ cm^?2, which correspond to the mean dimensionless distance between the particles r _s =8. This value far exceeds the threshold values observed for 3D systems (r _s ≈2), as well as the values obtained for quantum wells in previous studies. The problem of measuring the concentration of low-density 2D charge carriers in photoexcitation conditions is solved by applying the method of optical detection of the dimensional magnetoplasma resonance. This method provides reliable measurements of the density of a 2D system to the values about 10⁹ cm^?2.     

Nuclear matter approach to the heavy-ion optical potential: (II). Imaginary part

The heavy-ion optical potentials are constructed in a nuclear matter approach, for the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O and ⁴⁰Ca + ⁴⁰Ca elastic scattering at the incident energies per nucleon E^lab/A ? 45 MeV. The energy density formalism is employed assuming that the complex energy density of colliding heavy ions is a functional of the nucleon density ?(r), the intrinsic kinetic energy density τ⁽²⁾(r) and the average momentum of relative motion per nucleon K_r(≦ 1.5 fm^?1). The complex energy density is numerically evaluated for the two units of colliding nuclear matter with the same values of ρ, τ⁽²⁾ and K_r. The Bethe-Goldstone equation is solved for the corresponding Fermi distribution in momentum space using the Reid soft-core interaction. The “self-consistent” single-particle potential for unoccupied states which is continuous at the Fermi surface plays a crucial role to produce the imaginary part. It is found that the calculated optical potentials become more attractive and absorptive with increasing incident energy. The elastic scattering and the reaction cross sections are in fair agreement with the experimental data.     

Effective Field Theory of 3He

We examine the effects of the long range Coulomb force on the three-body contact interaction in a pionless effective theory of ³He. The corresponding interaction in ³H exhibits limit-cycle behavior and we show that this is not altered by the 1/r singularity of the potential.