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Generating functional and Green's function hierarchy of the Ising model

✍ Scribed by F Schwabl

Publisher
Elsevier Science
Year
1969
Tongue
English
Weight
738 KB
Volume
54
Category
Article
ISSN
0003-4916

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✦ Synopsis

The generating functional of the lsing model is studied. Equations of motion for the generating functional and the hierarchy of Green's functions are derived. These equations resemble a scalar field theory with nonlinear derivative coupling. Such a formulation bridges the gap between the Ising model as a configurational problem and field theoretic models of phase transitions. Only for the one dimensional lattice one can solve the equations exactly. In two and three dimensions several decoupling schemes are investigated: lowest order Hartree, Hartree approximation and a truncation, which includes also the four point function. The results are compared with graphical summations and other approximate theories.

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