  In this article we show the convergence of a loop ensemble of interfaces in
the FK Ising model at criticality, as the lattice mesh tends to zero, to a
unique conformally invariant scaling limit. The discrete loop ensemble is
described by a canonical tree glued from the interfaces, which then is shown to
converge to a tree of branching SLEs. The loop ensemble contains unboundedly
many loops and hence our result describes the joint law of infinitely many
loops in terms of SLE type processes, and the result gives the full scaling
limit of the FK Ising model in the sense of random geometry of the interfaces.
  Some other results in this article are convergence of the exploration process
of the loop ensemble (or the branch of the exploration tree) to
SLE$(\kappa,\kappa-6)$, $\kappa=16/3$, and convergence of a generalization of
this process for $4$ marked points to SLE$[\kappa,Z]$, $\kappa=16/3$, where $Z$
refers to a partition function. The latter SLE process is a process that can't
be written as a SLE$(\kappa,\rho_1,\rho_2,\ldots)$ process, which are the most
commonly considered generalizations of SLEs.
