Green's function approach to the Ising model

1969 ◽  
Vol 47 (7) ◽  
pp. 769-777 ◽  
Author(s):  
K. C. Lee ◽  
Robert Barrie
Keyword(s):  
Ising Model ◽  
Green’S Function ◽  
Green's Function ◽  
Body Problem ◽  
Equations Of Motion ◽  
Function Technique ◽  
Many Body ◽  
One Dimensional ◽  
Spinless Fermion ◽  
The One

It is shown that the spin [Formula: see text] Ising model can be formulated as a spinless fermion many-body problem and that the Green's function technique can be applied to it. The hierarchy of Green's function equations of motion terminates at the (q + 1)-particle Green's function, where q is the coordination number. This finite number of equations yields Fisher's transformation of correlations. The technique discussed in this paper can be used to obtain exact results for the one-dimensional Ising model.

A moment theorem for resonance line shapes arising from decoupled Green's function equations

1969 ◽  
Vol 47 (7) ◽  
pp. 787-793 ◽  
Author(s):  
Barry Frank ◽  
R. Barrie
Keyword(s):  
Ising Model ◽  
Green’S Function ◽  
Green's Function ◽  
Resonance Line ◽  
Delta Function ◽  
One Dimensional ◽  
Line Shapes ◽  
The One

A theorem is derived which enables one to bypass quadrature in the calculation of moments of a resonance line obtained from any decoupling of the Green's function hierarchy of equations. These moments are those of the resonance line as expressed in terms of delta-function peaks prior to smearing. A comparison with exact theoretical moments then provides a test of the decoupling procedure as distinct from the smearing technique. The method is illustrated by application to the one-dimensional Ising model.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

A reformulation of the dimer problem

1968 ◽  
Vol 46 (15) ◽  
pp. 1681-1684 ◽  
Author(s):  
R. W. Gibberd
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Green’S Function ◽  
Green's Function ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Function Technique ◽  
Value Of Time ◽  
Expectation Value

It is shown that the partition function of the generalized dimer problem can be formulated in terms of a vacuum-to-vacuum expectation value of time-ordered operators. This expression is then evaluated by using Green's function technique, which has already been used in conjunction with the Ising model and ferroelectric problem.

scholarly journals Exact Green's Function for the Finite Rectangular Potential Well in One Dimension

1985 ◽  
Vol 40 (4) ◽  
pp. 379-382 ◽  
Author(s):  
R. Baltin
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Free Particle ◽  
One Dimension ◽  
Potential Well ◽  
Complex Energy ◽  
One Dimensional ◽  
Special Cases ◽  
The One ◽  
Energy Plane

For the one-dimensional potential well with finite height V0( V0 > 0 or V0 < 0) the exact Green's function G is calculated by solving the differential equation. The poles of G in the complex energy plane are shown to coincide with the solutions to the Schrödinger eigenvalue equation for this potential. The well-known Green's functions for the special cases of the free particle and of the particle in an infinitely high potential box are recovered.

Sign in / Sign up

Export Citation Format

Share Document