= Self-dual parameter of the random-cluster model
{title2=$p_{\mathrm{sd}}(q)=\sqrt q/(1+\sqrt q)$}
Planar random-cluster duality relates edge odds by $[p/(1-p)][p^*/(1-p^*)]=q$. The fixed point $p=p^*$ has odds $\sqrt q$, giving the displayed parameter. A self-dual parameter does not by itself establish a critical threshold on an arbitrary <planar graph>. At this parameter the <symmetric cluster weight at the self-dual parameter> makes the primal-dual cluster counts explicit.
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