= Decorated-spin occupation insertion
{title2=$\langle\tau^2\rangle=\operatorname{tr}(QV^{L-1})/\operatorname{tr}V^L$}
An <observable> on a <spin> removed by <Decimation of an alternating mixed-spin chain>[decimation] is inserted before its local sum. For $\tau^2$, replace $V_{st}=\sum_\tau e^{\beta\tau(J_1s+J_2t)}$ by $Q_{st}=\sum_\tau\tau^2e^{\beta\tau(J_1s+J_2t)}=2\cosh[\beta(J_1s+J_2t)]$. Contracting the unchanged ring gives the displayed <Expectation>[thermal expectation value]. In the infinite chain it becomes $v_+^{\mathsf T}Qv_+/\lambda_+$ for <Normalization>[normalized] dominant <eigenvector> $v_+$.
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