Previous studies of the commutator-type Green's functions are extended to the anticommutator type. The existence of an $\ensuremath{\omega}=0$ pole in the latter but not former case is demonstrated. Its residue is simply related to the long-time behavior of the corresponding correlation function.

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Physics Letters A

Zero-frequency behavior of thermodynamic green's functions

Herbert B. Callen, Robert H. Swendsen, Raza A. Tahir-Kheli

Published Oct 1, 1967• 26 citations

Publisher

DOI: 10.1016/0375-9601(67)90012-6

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{\mathit{S}}_{0}^{\mathit{z}}

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

〉 and 〈

{\mathit{S}}_{0}^{+}

${\mathit{S}}_{\mathit{n}}^{\mathrm{\ensuremath{-}}}$〉 under the constraint of 〈

{\mathit{S}}^{\mathit{z}}

〉=0, from which a set of self-consistent equations are derived and solved numerically. The thermodynamic properties such as internal energy, specific heat, and zero-field parallel susceptibility are calculated. Our results predict the correct behavior for the correlation functions and thermodynamic quantities in the entire temperature region, in agreement both with the exact numerical results on the finite chain and the experimental data.