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Perturbing a CFT by a relevant operator on a half space and letting theperturbation flow to the far infrared we obtain an RG interface between the UVand IR CFTs. If the IR CFT is trivial we obtain an RG boundary condition. Thespace of massive perturbations thus breaks up into regions labelled byconformal boundary conditions of the UV fixed point. For the 2D critical Isingmodel perturbed by a generic relevant operator we find the assignment of RGboundary conditions to all flows. We use some analytic results but mostly relyon TCSA and TFFSA numerical techniques. We investigate real as well asimaginary values of the magnetic field and, in particular, the RG trajectorythat ends at the Yang-Lee CFT. We argue that the RG interface in the lattercase does not approach a single conformal interface but rather exhibitsoscillatory non-convergent behaviour.

RG boundaries and interfaces in Ising field theory