  We consider the Cauchy problem for the defocusing modified Korteweg-de Vries
(mKdV) equation with non-zero boundary conditions, which can be characterized
using a Riemann-Hilbert (RH) problem through the inverse scattering transform.
Using the $\bar\partial$ generalization of the Deift-Zhou nonlinear steepest
descent approach, combined with the double scaling limit technique, we obtain
the long-time asymptotics of the solution of the Cauchy problem in the
transition region $|x/t+6|t^{2/3}< C$ with $C>0$. The asymptotics is expressed
in terms of the solution of the second Painlev\'{e} transcendent.
