Freezing transition in the Ising model without internal contours

We consider the low temperature Ising model in a uniform mag netic field h > 0 with minus boundary conditions and conditioned on having no internal co ntours. This simple contour model defines a non-Gibbsian spin state. For la rge enough magnetic fields (h > h(c)) this state is concentrated on the sin gle spin configuration of all spins up. For smaller values (h less than or equal to h(c)), the spin state is non-trivial. At the critical point h(c) n ot equal 0 the magnetization jumps discontinuously. Freezing provides also an example of a translation invariant weakly Gibbsian state which is not al most Gibbsian.