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