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We consider global 2-SLE$_{\kappa}$ $(\eta_1, \eta_2)$ in a topologicalrectangle with $\kappa\in (4,8)$. We derive the law of a random hitting pointof the curves and show that, conditional on this random hitting point, the pairof two curves has the same law as Gaussian free field flow lines with properboundary data. Using a similar idea, we derive the asymptotic of theprobability for $\eta_1\cap\eta_2=\emptyset$. As an application, we derive theasymptotic of the probability for the existence of two disjoint open paths incritical FK-Ising model.

Decomposition of global 2-SLE for $\kappa\in (4,8)$ and an application for critical FK-Ising model