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Journal of Mathematical Physics

Green's Functions for the Ising Chain

Iwo Białynicki‐Birula, J. Piasecki

Published Oct 1, 1968• 2 citations
Publisher

Abstract

The Ising chain is represented as a system of fermions interacting through two-particle forces. All thermodynamic Green's functions are calculated exactly in this model. They exhibit many properties expected on the basis of general theory for Green's functions of the interacting particles.
DOI
10.1063/1.1664489

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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.
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