  Quantum critical behavior in the two-impurity Kondo model requires the
distinct separation of two scales, T_K >> T*, where T_K is the Kondo
temperature and T* is the scale at which the system renormalizes away from the
quantum critical point to a stable Fermi liquid fixed point. We provide a
derivation of T* based on the renormalization group to lowest order. This
result is confirmed by a numerical renormalization group (NRG) analysis which
supplements the analytic derivation with additional quantitative precision. The
form of the low-energy Fermi liquid fixed point is derived and subsequently
confirmed by the NRG. We discuss implications for series double quantum dot
systems.
