= Random-cluster inverse correlation length
{title2=$\alpha=\inf_{n\ge1}-n^{-1}\log\phi^1_{p,q}(0\leftrightarrow ne_1)$}
<Positive association of random variables> and <translation invariance> give $C_{m+n}\ge C_mC_n$ for axis connection <probabilities>. The <Fekete lemma> applied to $-\log C_n$ proves the displayed <limit of a sequence> and the bound $C_n\le e^{-n\alpha}$. The lower single-edge conditional bound gives $C_n\ge[p/(p+q(1-p))]^n$, so the decay rate is finite and nonnegative. It may be zero.
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