= Decimation of an alternating mixed-spin chain
{title2=$V_{st}=1+2\cosh[\beta(J_1s+J_2t)]$}
For <Ising spins> $s,t=\pm1$ separated by a decorating <spin> $\tau=0,\pm1$, summing its <Boltzmann weights> removes that <spin> exactly. If its two <exchange interactions> are $-\tau(J_1s+J_2t)$, the effective <transfer matrix> has entries $1+2\cosh[\beta(J_1s+J_2t)]$. Its <eigenvalues> are $\lambda_+=2+4\cosh(\beta J_1)\cosh(\beta J_2)$ and $\lambda_-=4\sinh(\beta J_1)\sinh(\beta J_2)$. A transfer step contains two physical sites, so the limiting <Helmholtz free energy> per site is $-(2\beta)^{-1}\log\lambda_+$.
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