= Monotonicity of random-cluster critical probability in cluster weight
{title2=$q_1\le q_2\Longrightarrow p_c(q_1)\le p_c(q_2)$}
The finite-volume <random-cluster weight monotonicity> passes to consistently wired or free infinite-volume measures for finite increasing connection events. Decreasing these events to origin-to-infinity connectivity yields $\theta(p,q_1)\ge\theta(p,q_2)$ for $q_1\le q_2$. The corresponding supercritical parameter sets are nested, and hence $p_c(q_1)\le p_c(q_2)$.
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