Thermodynamic perturbation theory is described in terms of temperature-dependent Green functions. The relationship of these functions with time-temperature-dependent Green functions and with correlation functions is discussed and some of their analytic properties are derived. The chain of coupled equations forming the equations of motion of the Green functions is derived and is written in terms of functional derivatives. Two examples of the use of Green functions, discussions of the sharpness of the Fermi surface and of neutron scattering from liquid helium, are given. The use of Green functions in the theory of relaxation phenomena is described.Thermodynamic perturbation theory is described in terms of temperature-dependent Green functions. The relationship of these functions with time-temperature-dependent Green functions and with correlation functions is discussed and some of their analytic properties are derived. The chain of coupled equations forming the equations of motion of the Green functions is derived and is written in terms of functional derivatives. Two examples of the use of Green functions, discussions of the sharpness of the Fermi surface and of neutron scattering from liquid helium, are given. The use of Green functions in the theory of relaxation phenomena is described.

Reports on Progress in PhysicsJan 1, 196413 citations

Method for breaking chains of equations for green's functions

R. Kh. Sabirov

Russian Physics JournalAug 1, 19960 citations

Thermodynamic properties of one-dimensional spin-1 antiferromagnetic Heisenberg chains: Green’s-function approach

Shu-Qing Bao, Hu Zhao, Jue-Lian Shen +1 more

The one-dimensional spin-1 Heisenberg antiferromagnetic chains are studied by a generalized two-time Green's-function method at finite temperature. 〈 ${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ 〉 is set to zero at each site to guarantee the lack of the long-range order in the one-dimensional Heisenberg system. The Green's functions are decoupled in terms of the correlation functions of spin operators. A set of self-consistent equations of the correlation functions are derived and solved numerically. Correlation functions of spin operators, thermodynamic properties such as the internal energy, and specific heat in the entire temperature region are obtained. The Haldane gap in the excitation spectrum appears naturally in the analytical result. When k is zero, there is a gap 2\ensuremath{\Delta}, which is 1.0J and close to the theoretical result of White and Huse. And there is a broad maximum in the temperature dependence of the specific heat. The properties of the thermodynamic quantities are consistent with the numerical results on the finite chains. \textcopyright{} 1996 The American Physical Society.The one-dimensional spin-1 Heisenberg antiferromagnetic chains are studied by a generalized two-time Green's-function method at finite temperature. 〈${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$〉 is set to zero at each site to guarantee the lack of the long-range order in the one-dimensional Heisenberg system. The Green's functions are decoupled in terms of the correlation functions of spin operators. A set of self-consistent equations of the correlation functions are derived and solved numerically. Correlation functions of spin operators, thermodynamic properties such as the internal energy, and specific heat in the entire temperature region are obtained. The Haldane gap in the excitation spectrum appears naturally in the analytical result. When k is zero, there is a gap 2\ensuremath{\Delta}, which is 1.0J and close to the theoretical result of White and Huse. And there is a broad maximum in the temperature dependence of the specific heat. The properties of the thermodynamic quantities are consistent with the numerical results on the finite chains. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterJan 1, 199624 citations

Internal consistency of the method of two-time thermal Green's functions

M. F. Sarry

Russian Physics JournalJul 1, 19800 citations

The one-dimensional spin-1 Heisenberg antiferromagnetic chains are studied by a generalized two-time Green's-function method at finite temperature. 〈

{\mathit{S}}_{\mathit{i}}^{\mathit{z}}

〉 is set to zero at each site to guarantee the lack of the long-range order in the one-dimensional Heisenberg system. The Green's functions are decoupled in terms of the correlation functions of spin operators. A set of self-consistent equations of the correlation functions are derived and solved numerically. Correlation functions of spin operators, thermodynamic properties such as the internal energy, and specific heat in the entire temperature region are obtained. The Haldane gap in the excitation spectrum appears naturally in the analytical result. When k is zero, there is a gap 2\ensuremath{\Delta}, which is 1.0J and close to the theoretical result of White and Huse. And there is a broad maximum in the temperature dependence of the specific heat. The properties of the thermodynamic quantities are consistent with the numerical results on the finite chains. \textcopyright{} 1996 The American Physical Society.