The Green's-function method is employed to study the two-dimensional system of classical $\mathrm{O}(N)$ -vector spins. The second-order double-time retarded Green's functions of the corresponding quantum Hamiltonian system on a one-dimensional lattice are decoupled approximately in a selfconsistent manner. The expressions for the mass gap and the spin-correlation function thus obtained reproduce the known exact results in the large- $N$ limit and in the strong-coupling region. Some directions are discussed to improve the present method in the region of weak coupling with $N$ not large.The Green's-function method is employed to study the two-dimensional system of classical $\mathrm{O}(N)$-vector spins. The second-order double-time retarded Green's functions of the corresponding quantum Hamiltonian system on a one-dimensional lattice are decoupled approximately in a selfconsistent manner. The expressions for the mass gap and the spin-correlation function thus obtained reproduce the known exact results in the large-$N$ limit and in the strong-coupling region. Some directions are discussed to improve the present method in the region of weak coupling with $N$ not large.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsApr 15, 19842 citations

Spin Systems and the Green Functions Method

WORLD SCIENTIFIC eBooksMar 5, 20170 citations

Statistical diagonalization of the Hamiltonian with interaction in the Green function theory

充福地, 一夫椎木

A new method to obtain the knowledge for the ground state energy as well as one for the elementary excitation energy in an interacting many particle system is considered from the intuitive approach in the double time Green function theory.Using this method of approach the statistical diagonalization which may include properly the effects of temperature and other external fields can be performed when the Green functions are solved by an appropriate approximation, and the physical meaning of the results is considered.The application to the Heisenberg antiferromagnet is shown to lead the temperature and external magnetic field dependent results in the approximation of Tyablikov decoupling.A new method to obtain the knowledge for the ground state energy as well as one for the elementary excitation energy in an interacting many particle system is considered from the intuitive approach in the double time Green function theory.Using this method of approach the statistical diagonalization which may include properly the effects of temperature and other external fields can be performed when the Green functions are solved by an appropriate approximation, and the physical meaning of the results is considered.The application to the Heisenberg antiferromagnet is shown to lead the temperature and external magnetic field dependent results in the approximation of Tyablikov decoupling.

Proceedings of the Fujihara Memorial Faculty of Engineering Keio UniversityJan 1, 19700 citations

Method of functional integration in the theory of spin systems

I. O. Vakarchuk, Yu. K. Rudavskii

Theoretical and Mathematical PhysicsNov 1, 198119 citations

New methods in the theory of quantum spin systems

V Ulyanov

Physics ReportsJul 1, 1992167 citations

Perturbation theory for double-time temperature-dependent Green functions

Sergei Vladimirovich Tyablikov, В. Л. Бонч-Бруевич

(by translator) A perturbation theory is developed for normal many-particle systems by expanding the inverse of the advanced and retarded Green functions. Both systems with direct interactions and systems with interactions through a quantum field are considered. For the former, the infinite set of coupled equations is written down and the various methods of decoupling discussed. Systems with weak, hard sphere type, or coulomb interactions are considered and the connections with other methods discussed. For systems with quantum field interactions, the chain of equations involves both fermion and boson Green functions and the first approximation can be much better than in earlier cases. This latter approach seems to be more convenient when collective oscillations are important.(by translator) A perturbation theory is developed for normal many-particle systems by expanding the inverse of the advanced and retarded Green functions. Both systems with direct interactions and systems with interactions through a quantum field are considered. For the former, the infinite set of coupled equations is written down and the various methods of decoupling discussed. Systems with weak, hard sphere type, or coulomb interactions are considered and the connections with other methods discussed. For systems with quantum field interactions, the chain of equations involves both fermion and boson Green functions and the first approximation can be much better than in earlier cases. This latter approach seems to be more convenient when collective oscillations are important.

Advances In PhysicsOct 1, 196256 citations

The Green's-function method is employed to study the two-dimensional system of classical

\mathrm{O}(N)

-vector spins. The second-order double-time retarded Green's functions of the corresponding quantum Hamiltonian system on a one-dimensional lattice are decoupled approximately in a selfconsistent manner. The expressions for the mass gap and the spin-correlation function thus obtained reproduce the known exact results in the large-

N

limit and in the strong-coupling region. Some directions are discussed to improve the present method in the region of weak coupling with

N

not large.