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Conformal interfaces separating two conformal field theories (CFTs) providemaps between different CFTs, and naturally exist in nature as domain wallsbetween different phases. One particularly interesting construction of aconformal 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 wallcan be generated by a specific deformation which triggers an RG flow towardsits adjacent Virasoro minimal model $\mathcal{M}_{k+2,k+1}$ with thedeformation turned on over part of the space. An algebraic construction of thisdomain wall was proposed by Gaiotto in \cite{Gaiotto:2012np}. In this paper, wewill provide a study of this RG domain wall for the minimal case $k=2$, whichcan be thought of as a nonperturbative check of the construction. In this casethe wall is separating the Tricritical Ising Model (TIM) CFT and the IsingModel (IM) CFT. We will check the analytical results of correlation functionsfrom the RG brane construction with the numerical density matrixrenormalization group (DMRG) calculation using a lattice model proposed in\cite{Grover:2012bm,Grover:2013rc}, and find a perfect agreement. We comment onpossible experimental realizations of this RG domain wall.

CFT and Lattice Correlators Near an RG Domain Wall between Minimal Models