Green’s-function theory of the anisotropic Heisenberg model in a transverse field

1987 ◽  
Vol 36 (1) ◽  
pp. 266-274 ◽  
Author(s):  
Edward B. Brown
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Heisenberg Model ◽  
Function Theory ◽  
Transverse Field ◽  
Anisotropic Heisenberg Model

THE FERMIONIC GREEN'S FUNCTION THEORY FOR CALCULATION OF MAGNETIZATION

2002 ◽  
Vol 16 (25) ◽  
pp. 3803-3816 ◽  
Author(s):  
HUAI-YU WANG ◽  
KE-QIU CHEN ◽  
EN-GE WANG
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Heisenberg Model ◽  
Function Theory ◽  
Present Theory ◽  
Higher Order ◽  
Statistical Average ◽  
Universal Formula ◽  
Anisotropic Heisenberg Model ◽  
Three Components

The fermionic Green's function theory of Heisenberg-like Hamiltonian is presented in this paper. For the case that the Hamiltonian is isotropic and the higher-order Green's function is asymmetrically decoupled, the present theory is equivalent to the bosonic Green's function theory. When the Hamiltonian is anisotropic and the higher-order Green's function is symmetrically decoupled, it gives the universal formula to calculate the three components of statistical average of spin operators which one encountered when dealing with ferromagnetic or ferroelectric systems described by anisotropic Heisenberg model or pseudospin model respectively. Both cases of <Sz> ≠ 0 and <Sz> = 0 are investigated. Explicit expressions are derived for spin value S = 1/2, 1, 3/2, 2, and 5/2. General expressions for any S value are suggested.

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