  Using previous results from boundary conformal field theory and
integrability, a phase diagram is derived for the 2 dimensional Ising model at
its bulk tri-critical point as a function of boundary magnetic field and
boundary spin-coupling constant. A boundary tri-critical point separates phases
where the spins on the boundary are ordered or disordered. In the latter range
of coupling constant, there is a non-zero critical field where the
magnetization is singular. In the former range, as the temperature is lowered,
the boundary undergoes a first order transition while the bulk simultaneously
undergoes a second order transition.
