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Quantum critical behavior in the two-impurity Kondo model requires thedistinct separation of two scales, T_K >> T*, where T_K is the Kondotemperature and T* is the scale at which the system renormalizes away from thequantum critical point to a stable Fermi liquid fixed point. We provide aderivation of T* based on the renormalization group to lowest order. Thisresult is confirmed by a numerical renormalization group (NRG) analysis whichsupplements the analytic derivation with additional quantitative precision. Theform of the low-energy Fermi liquid fixed point is derived and subsequentlyconfirmed by the NRG. We discuss implications for series double quantum dotsystems.

Crossover in the two-impurity Kondo model induced by direct charge tunneling