Random-cluster negative-correlation conjecture

Let $G=(V,E)$ be a graph, let $\boldsymbol{x}=x_e:e otin E$ be positive edgeweights, and let the random cluster model on $G$ have parameter $q$. For distinct edges $e,f otin E$, write $\mathcal{J}_e$ and $\mathcal{J}_f$ for the events that the corresponding edges are open. Random-cluster negative-correlation conjecture. The random cluster model is negatively correlated for $0\leq q\leq 1$:

$$\mu(\mathcal{J}_e\cap\mathcal{J}_f)\leq\mu(\mathcal{J}_e)\mu(\mathcal{J}_f).$$

This conjecture concerns negative association of edge-open events in the random cluster model. The supplied text gives no resolution status.