  Conformal interfaces separating two conformal field theories (CFTs) provide
maps between different CFTs, and naturally exist in nature as domain walls
between different phases. One particularly interesting construction of a
conformal interface is the renormalization group (RG) domain wall between CFTs.
For a given Virasoro minimal model $\mathcal{M}_{k+3,k+2}$, an RG domain wall
can be generated by a specific deformation which triggers an RG flow towards
its adjacent Virasoro minimal model $\mathcal{M}_{k+2,k+1}$ with the
deformation turned on over part of the space. An algebraic construction of this
domain wall was proposed by Gaiotto in \cite{Gaiotto:2012np}. In this paper, we
will provide a study of this RG domain wall for the minimal case $k=2$, which
can be thought of as a nonperturbative check of the construction. In this case
the wall is separating the Tricritical Ising Model (TIM) CFT and the Ising
Model (IM) CFT. We will check the analytical results of correlation functions
from the RG brane construction with the numerical density matrix
renormalization group (DMRG) calculation using a lattice model proposed in
\cite{Grover:2012bm,Grover:2013rc}, and find a perfect agreement. We comment on
possible experimental realizations of this RG domain wall.
