= Connective-constant Peierls bound
{title2=$p_c\leq1-\mu^{-1}$}
Independent <bond percolation> on the <square lattice> satisfies $p_c\leq1-\mu^{-1}$, where $\mu$ is its <connective constant>. If $(1-p)\mu<1$, closed dual <graph cycles> have a summable large-length tail: their counts are bounded by a polynomial factor times the count of <self-avoiding walks>. Conditioning a sufficiently large finite box to be open excludes short enclosing <graph cycles> without changing the law of the remaining <edges>. With positive conditional <probability> no enclosing closed dual <graph cycle> remains, so the origin belongs to an <infinite percolation cluster>.
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