  We establish a renormalization group approach which is implemented on the
degrees of freedom defined by the overlap of two replicas to determine the
critical fixed point and to extract four critical exponents for the phase
transition of the three-dimensional Edwards-Anderson model. In addition, we
couple the overlap order parameter to a fictitious field and introduce it
within the two-replica Hamiltonian of the system to study its explicit
symmetry-breaking with the renormalization group. Overlap transformations do
not require a renormalization of the random couplings of a system to extract
the critical exponents associated with the relevant variables of the
renormalization group. We conclude by discussing the applicability of such
transformations in the study of any phase transition which is fully
characterized by an overlap order parameter.
