Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

physica status solidi (b)

A decoupling procedure for green functions: Test at the ising model and application to an extended hubbard model

Dieter Ihle, B. Lorenz

Published Nov 1, 1973• 18 citations
Publisher

Abstract

Abstract A decoupling procedure for the double‐time three‐particle Green functions is presented. The formalism is tested at the spin ½ nearest‐neighbour interaction Ising model yielding more accurate results than Bethe's first approximation. The decoupling procedure is applied to the problem of electron‐charge ordering on the basis of an extended Hubbard model investigated by Bari, the corresponding phase diagram being calculated.

DOI
10.1002/pssb.2220600135

Related papers

Green function decoupling scheme for spin-spin correlations in Ising model: Example of partly ordered binary alloy

M. S. Magdoń-Maksymowicz, A.Z. Maksymowicz

In this paper we present Green function technique applied to calculations of spin-spin correlations in systems governed by Ising Hamiltonian. This offers approximate yet reasonably accurate analytical results, as an alternative approach to direct computer simulation. Local spin operators are represented in terms of particle operators for fermions. Chain of Green functions for local magnetization on given site involves nearest neighbors and it is decoupled at the next-nearest-neighbors level. Therefore, still accounts at the lowest level for magnetic correlations between nearest neighbors. This technique was applied to binary alloy A x B 1-x with given atomic short range order. Calculations for stoichiometric x=1/2 composition show how temperature dependence of magnetization and spin-spin correlations are modified when atomic order parameter changes. We scanned this parameter from the case of ordered binary alloy, via random alloy, to clusterlike structure. In model calculations we (a) confirm characteristic λ -like shape of the magnetic specific heat near Curie temperature and (b) recover essential results of exact, two-dimensional Ising model. This supports our claim of usefulness of such analytical approach, which is easy and flexible to describe different geometries (clusters, thin films) and conditions imposed on spins located on specific atoms (spins partly pinned on the surface atoms).

Physical Review E•May 26, 2010•1 citation

A justification of Hubbard's decoupling scheme

D K Ghosh

Using Sawada's Green function technique, which separates various orders of correlations, the author solves the Hubbard model and shows that the single particle Green function has the same structure as Hubbard's solution using the double time Green function technique. The demonstration helps to clarify the uncertainty with regard to the decoupling procedure.

Journal of Physics C Solid State Physics•Jun 28, 1971•2 citations

A Decoupling Procedure for Green Functions: Test at the Ising Model and Application to an Extended Hubbard Model

Dieter Ihle, B. Lorenz

De Gruyter eBooks•Dec 31, 1973•0 citations

Roth's method and moment conservation of the spectral weight function for the neutral Hubbard model

E. Heiner

Abstract The method of Roth for the calculation of a (2 × 2 ) Green's function matrix is equivalent to the moment technique for the spectral weight function up to the fourth order. The method can be extended in order to derive a set of orthogonalized operators. With this method a selfconsistent calculation of the single‐particle Green's function and all important correlation functions of nearest neighbour sites is possible for the neutral Hubbard model. The results agree for a sc lattice in the strong correlation region at arbitrary temperatures with those of Shiba and Pincus for finite Hubbard systems. An antiferromagnetic coupling of neighboured lattice sites is increasing with a decrease of the temperature, a metalinsulator transition does not exist in this two‐pole approximation.

physica status solidi (b)•Sep 1, 1976•8 citations

Green's-Function Analysis of the Ising Ferromagnet

F. Burr Anderson

The method of the two-time temperature-dependent Green's function has been used to analyze the Ising model of a ferromagnet in an external magnetic field. The selection of a particular Green's function enables us to write an exact expression for the equation of motion. We are then led to a differential difference equation for the correlation function corresponding to the Green's function. No decoupling assumptions have been made, so the equation is exact for both arbitrary spin and range of interaction. It is shown how various approximate theories may be extracted from our formalism. The exact differential difference equation may be reduced to a partial differential equation. The latter form allows us to generate relations among the magnetization and spin-spin correlation functions. These relations are given in detail for the case of spin \textonehalf{} and $z$ nearest neighbors.

Physical review. B, Solid state•Jun 1, 1971•9 citations

HIGH-DENSITY EXPANSION FOR THE EXTENDED HUBBARD MODEL

M. Bartkowiak

The Green’s-function diagrammatic high-density expansion technique for Hubbard’s operators is constructed and applied to the extended Hubbard model. The electron Green’s functions and the band structure of the ground state for arbitrary electron density are calculated in the zeroth-order in 1/z. The phase diagram, staggered magnetic susceptibility and the Néel temperature for the half-filled band case are derived in the first order of the high-density expansion. Connections of the high-density and linked cluster expansions are also discussed.

International Journal of Modern Physics B•Oct 1, 1987•7 citations
Abstract A decoupling procedure for the double‐time three‐particle Green functions is presented. The formalism is tested at the spin ½ nearest‐neighbour interaction Ising model yielding more accurate results than Bethe's first approximation. The decoupling procedure is applied to the problem of electron‐charge ordering on the basis of an extended Hubbard model investigated by Bari, the corresponding phase diagram being calculated.
In this paper we present Green function technique applied to calculations of spin-spin correlations in systems governed by Ising Hamiltonian. This offers approximate yet reasonably accurate analytical results, as an alternative approach to direct computer simulation. Local spin operators are represented in terms of particle operators for fermions. Chain of Green functions for local magnetization on given site involves nearest neighbors and it is decoupled at the next-nearest-neighbors level. Therefore, still accounts at the lowest level for magnetic correlations between nearest neighbors. This technique was applied to binary alloy A x B 1-x with given atomic short range order. Calculations for stoichiometric x=1/2 composition show how temperature dependence of magnetization and spin-spin correlations are modified when atomic order parameter changes. We scanned this parameter from the case of ordered binary alloy, via random alloy, to clusterlike structure. In model calculations we (a) confirm characteristic λ -like shape of the magnetic specific heat near Curie temperature and (b) recover essential results of exact, two-dimensional Ising model. This supports our claim of usefulness of such analytical approach, which is easy and flexible to describe different geometries (clusters, thin films) and conditions imposed on spins located on specific atoms (spins partly pinned on the surface atoms).
Abstract The method of Roth for the calculation of a (2 × 2 ) Green's function matrix is equivalent to the moment technique for the spectral weight function up to the fourth order. The method can be extended in order to derive a set of orthogonalized operators. With this method a selfconsistent calculation of the single‐particle Green's function and all important correlation functions of nearest neighbour sites is possible for the neutral Hubbard model. The results agree for a sc lattice in the strong correlation region at arbitrary temperatures with those of Shiba and Pincus for finite Hubbard systems. An antiferromagnetic coupling of neighboured lattice sites is increasing with a decrease of the temperature, a metalinsulator transition does not exist in this two‐pole approximation.
The method of the two-time temperature-dependent Green's function has been used to analyze the Ising model of a ferromagnet in an external magnetic field. The selection of a particular Green's function enables us to write an exact expression for the equation of motion. We are then led to a differential difference equation for the correlation function corresponding to the Green's function. No decoupling assumptions have been made, so the equation is exact for both arbitrary spin and range of interaction. It is shown how various approximate theories may be extracted from our formalism. The exact differential difference equation may be reduced to a partial differential equation. The latter form allows us to generate relations among the magnetization and spin-spin correlation functions. These relations are given in detail for the case of spin \textonehalf{} and zzz nearest neighbors.
The Green’s-function diagrammatic high-density expansion technique for Hubbard’s operators is constructed and applied to the extended Hubbard model. The electron Green’s functions and the band structure of the ground state for arbitrary electron density are calculated in the zeroth-order in 1/z. The phase diagram, staggered magnetic susceptibility and the Néel temperature for the half-filled band case are derived in the first order of the high-density expansion. Connections of the high-density and linked cluster expansions are also discussed.