Conformal Limits of Critical Square-Lattice Random-Cluster Interfaces

For every fixed $1\le q\le 4$, critical square-lattice random-cluster Dobrushin interfaces converge to chordal ${\mathrm{SLE}}_{\kappa (q)}$, where $\kappa (q)=4\pi /\arccos (-\sqrt{q}/2)$, and the complete nested plane loop collections converge to whole-plane ${\mathrm{CLE}}_{\kappa (q)}$. The results hold under uniform marked Jordan boundary approximation and retain loop multiplicities and traversals. At q = 1 we obtain Cardy's formula for square-lattice bond percolation with free boundary edges.