  In the second article of this series, we establish the convergence of the
loop ensemble of interfaces in the random cluster Ising model to a conformal
loop ensemble (CLE) --- thus completely describing the scaling limit of the
model in terms of the random geometry of interfaces. The central tool of the
present article is the convergence of an exploration tree of the discrete loop
ensemble to a branching SLE$(16/3,-2/3)$. Such branching version of the
Schramm's SLE not only enjoys the locality property, but also arises logically
from the Ising model observables.
