Show that for a one-dimensional, field-free Ising model [ overline{sigma_{k} sigma_{l} sigma_{m} sigma_{n}}={tanh beta J}^{n-m+l-k}, ] where
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Show that for a one-dimensional, field-free Ising model
\[
\overline{\sigma_{k} \sigma_{l} \sigma_{m} \sigma_{n}}=\{\tanh \beta J\}^{n-m+l-k},
\]
where \(k \leq l \leq m \leq n\).
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