Order Green Functions Research Articles

Equation-of-motion treatment of the impurity Anderson model with a finite on-site Coulomb repulsion.

The impurity Anderson model with a finite Coulomb repulsion U has been studied by using the conventional equation-of-motion treatment for the f-electron Green's function. To get a closed equation, two types of approximations are incorporated. One is to neglect, in a large U limit, higher order Green's functions which involve three f-electron annihilation operators. The other is to linearize the equation of motion by using a projection operator method. The average valency ${\mathit{n}}_{\mathit{f}}$ and the spectral density of states (DOS) of f electrons are evaluated from the self-consistent equation for the Green's function. Results for ${\mathit{n}}_{\mathit{f}}$ are in good agreement with exact results of Bethe ansatz method, and the obtained spectral DOS exhibits a well-known three-peak structure. Effects of finite U and finite temperature on the spectral DOS are discussed.

Some Magnetic Properties of Thin Ferromagnetic Films in the Coherent Potential Approximation (S = 1)

AbstractThe coherent potential approximation method taking into account natural disorder connected with different states of spin components is applied to thin magnetic films with spin S = 1. The distribution of spontaneous magnetization as well as the temperature dependence of the critical temperature are obtained for b.c.c. (100) films. The results obtained using Tyablikov decoupling of higher order Green function are improved in relation to the Green function results obtained with the same decoupling procedure by including the line profiles of elementary excitations.

Green's Function Theory of the Two-Dimensional Ising Model –Derivation of the Logarithmic Divergence of the Specific Heat–

The S =1/2 Ising model for a square lattice is studied by means of the two-time Green's function method. A simple assumption is introduced associating with the rigorous relations among several spin correlation functions which are derived by this method and any approximations such as decoupling ones for the higher order Green's functions are not used. The specific heat obtained by using this assumption shows the logarithmic divergence just below and just above T c . It is ascertained that the theory issues only the error of order 1/ T 4 in the sum rule and in the susceptibility in the high temperature region.

Magnetically induced structural phase transitions

We consider the multiple spin density wave states of an itinerant model of a face centred cubic antiferromagnet. By investigating the total energies in the Hartree-Fock approximation and the susceptibility and higher order Green's functions in the random phase approximation we examine the transitions between the various MSDW phases. We show that for a special type of phase transition in which the spin components reorientate themselves we can have softening of phonons and the corresponding shear elastic constant in agreement with existing experiments. We suggest further experimental verification of our model.

SOME REMARKS CONCERNING THE FINITENESS OF N=4 SUPERSYMMETRIC YANG MILLS THEORIES

We carefully discuss the finiteness of SUSY YM N=4 in the light cone gauge, first at the one loop level by directly exhibiting the relevant terms of the lowest order Green functions and then at any loop order by using a recent treatment of the renormalization of general Yang-Mills theories in the light cone gauge. We point out the existence of a set of divergent Green functions which however do not contribute to observable quantities, thereby recovering consistency with formulations in other gauges.

Green Function Theory and its Global Structure

The Green function theory is successful in many fields of theoretical physics and the Bogoliubov-Gor'kov theory system is its important branch that involves many theoretical methods. In the last twenty years many papers have been published, but as all the equations of motion are coupled and their number is infinite, its global structure problem has not been investigated as yet. This paper is devoted to the study of its global structure, the exact decoupling problem, and the uniqueness and completeness problems. Some higher order spectral representation theorems and exact relationships between higher and lower order Green functions are obtained. Thus the equations of motion are decoupled exactly.In this paper it is proved that after cutting off the equations of motion are decoupled exactly and the solution of these equation systems may not be unique. It is also proved that if there is one solution satisfying all the Green function's equations, then there must be a solution set, all of them satisfy all the equations and its number is infinite and the differences between them are arbitrary.By adding some limitations to ImG(x) at the real axis a uniqueness theorem is proved.

Perturbation theory for QED bound states

A new method is presented for deriving a systematic perturbative expansion for QED bound states, which does not rely upon solving any new or old equation. The starting point is a given nonperturbative zeroth order Green's function, obtained by a suitable “relativistic dressing” of the nonrelativistic Green's function for the Schrödinger equation with Coulomb potential, which embodies the Coulombic bound states and is known. The comparison with the complete Green's function as given by standard perturbative QED gives a perturbative kernel which is then used for the expansion of the QED Green's function in terms of the given non-perturbative zeroth order Green's function.

Effects of biquadratic exchange interaction on dynamic susceptibility in Heisenberg ferromagnet

The Green function technique has been employed to study the dynamic susceptibility of a spin-1 system above the Curie temperature. Bilinear and biquadratic terms have been added in writing the Hamiltonian of the system. Higher order Green functions have been decoupled by RPA and Callen type decouplings. The dependence of spin wave energy, intensity and susceptibility on wavevector and biquadratic parameter have been studied.

Theory of Valence Transition

The valence transition phenomena occurring in rare-earth compounds are studied by using the periodic Anderson model with the electron-phonon coupling. This electron-phonon interaction G is treated in the Hartree-Fock approximation. The Coulomb repulsion U between f-electrons on the same site is taken to be ∞, and the decoupling method of Roth is used for the higher order Green function considering the mixing interaction to be small. We put the condition that the total number of electrons is a constant, and calculate the numbers of f- and d-electrons as functions of the original energy of f-electron by using the Green functions. The magnetic susceptibilities of both phases are also calculated, but the result is not good, showing the decoupling method used here is not appropriate for the calculation of magnetic properties.

Green's function theory for the one-dimensional antiferromagnet with antisymmetric exchange

The spin wave spectrum for the one-dimensional antiferromagnet with antisymmetric exchange is obtained from second order Green's function theory. There is a noticeable asymmetry in the spin wave dispersion curve, which has an effect on the static correlation function and the correlation length.

A Heisenberg antiferromagnet using second-order Green function theory

A two-sublattice Heisenberg antiferromagnet is treated using the second-order Green function formalism. The higher order Green functions are decoupled according to the random-phase approximations and the transition temperatures TN, where the paramagnetic staggered susceptibility diverges, and the nearest-neighbour correlation functions are calculated for systems having simple cubic and body centred cubic lattice structures and spin 1/2 to 7/2.

Introduction to an analysis of kinematical exciton levels

The possibility of the existence of kinematical levels for a multi-level exciton scheme is analysed and it is shown that such levels exist for all the values of the wave vector. This is the consequence of the fact that the exciton gap is much larger than the energy bandwidth. The existence of kinematical levels is proved using a more correct method of decoupling of higher order Green's functions in which pairing is performed not only for the same moments of time but for different moments as well. A matrix formulation of the system of equations for Green's function is proposed and the analysis is performed in this condensed form representing a sensible simplification which could be helpful for the analysis of other multilevel excitation systems, too.

Green function theory of Curie and order—order transitions in ferromagnetic systems

Dipolar critical temperatures in ferromagnetic systems with isotropic bilinear and biquadratic exchange are investigated by means of the Green function technique. Expressions are found for both the familiar Curie temperature, T c, and the less well known order-order transition temperature, T o , at which, under appropriate conditions, the magnetic ordering undergoes a change between fully aligned and canted ferromagnetism. At T = 0, a fully aligned state has < s i z = s for spin s and all lattice sites i, while a canted state has 〈 s i z 〉< s. It is shown independently of the Green function analysis that the T = 0 ground state is fully aligned if α, the ratio of biquadratic to bilinear exchange integrals, obeys −[2 s( s−1)] −1< α< [2 s 2−2 s+1] −1. The region below the lower limit is identified as the range in which canted ferromagnetism can occur and is a range that does not appear to have been considered previously via the Green function formalism. The temperature dependence of the magnetic ordering is investigated by means of the double-time temperature-dependent Green function formalism. A new decoupling scheme is derived and used to reduce higher order Green functions to lowest order. It is found that a canted state, occuring at low temperatures, undergoes a transition to a fully aligned state at a temperature T 0 and subsequently becomes disordered at temperature T c. Transitions to paramagnetism are found to be second order for α< α c and first order for α⩾ α c where α c is a critical value that depends on the atomic spin and weakly on the lattice structure. A phase diagram is given to illustrate the results, and a comparison is made with the corresponding results found in mean field theory.

On First Order Green Function Theory of S = 1/2 Transverse Ising Paramagnets

physica status solidi (b)Volume 75, Issue 2 p. K97-K99 Short Note On First Order Green Function Theory of S = 1/2 Transverse Ising Paramagnets G. Kamieniarz, G. Kamieniarz Solid State Division, Institute of Physics, A. Mickiewicz University, PoznańSearch for more papers by this author G. Kamieniarz, G. Kamieniarz Solid State Division, Institute of Physics, A. Mickiewicz University, PoznańSearch for more papers by this author First published: 1 June 1976 https://doi.org/10.1002/pssb.2220750243Citations: 2AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume75, Issue21 June 1976Pages K97-K99 RelatedInformation

Green function theory of dynamic conductivity

The transport processes can be discussed either by kinetic equation method or by correlation function method. Using the former, linear transport equations are developed for the study of dynamic conductivity of a quantum imperfect gas employing a resolution of BBGKY hierarchy using Green functions. From this transport equation a modified form of Kubo (correlation function) formula is obtained to show the equivalence between the two methods. This equivalence may be used for the justification of the concept of adiabatic switching of the field. The simple formula derived, gives the conductivity in terms of one-particle Green function, unlike the usual discussions which express it in higher order Green functions.

Spin waves in Heisenberg-ferromagnets above the critical point

Using a decoupling scheme for the second order Green's function expressions are derived for the dynamical susceptibility and for spin wave frequencies above the transition temperatureT c. The possible damping of the spin waves is discussed.

On first order green function theory with spin operators

On first order green function theory with spin operators

A Green's Function Theory of the Heisenberg Paramagnet

The second order Green's function is appli~d to discussion of the paramagnetic phase of the Heisenberg ferromagnet in the simple cubic lattice. In the case of spin one-half the products of the spin operators at the same lattice point are treated exactly. Analytical evaluations are performed at high temperatures to yield the results that (a) the nearest neighbour correlation function C1=1/24r-1+0(r-2), (b) the inverse susceptibility x-1=2-r-1 +O(r- 1), (c) the specific heat goes as r-2. These temperature dependences of the thermody­ namic quantities at high temperatures agree with the exact high temperature expansion theo­ ry up to the order of r 0 for x- 1• Numerical solutions yield the nearest neighbour correlation function at the Curie temperature C 1 (r.) =0.109 where the Curie temperature r.=0.245, which is compared with the Pade value r.=0.279. Near rc, x- 1 behaves as (r-r.)T, with r=l.95 ±0.01. '

On a Heisenberg Ferromagnet by a Second Order Green Function Approach

On a Heisenberg Ferromagnet by a Second Order Green Function Approach

The Green's Function Theory of the Spin 12 Ferromagnetic Crystal Utilizing Exchange Plus Dipole-Dipole Interaction Hamiltonian in the Single Excitation Limit

The Green's function technique (including dipole-dipole interactions) is applied to a bulk ferromagnet to obtain an expression for the magnetization at low temperatures. Only the lowest order Green's functions are used in the calculations, allowing only for single excitations. The result obtained is identical with the Holstein and Primakoff result and the Haas result, both of which were intended to be more inclusive than the present calculation—Holstein and Primakoff via diagonalizing the Hamiltonian, and Haas via symmetrically decoupling generated higher order Green's functions.