Freezing transition in the Ising model without internal contours (Q1969520)

The authors study statistical properties of a simple contour model arising as the low-temperature Ising model with minus boundary conditions and uniformly positive external magnetic field \(h\), from which all internal contours are excluded. The corresponding distribution is an example of non-Gibbsian spin state. It is shown that the model exhibits ``freezing transition'' in the magnetic field: for small values of \(h\), typical configurations contain many small contours, whereas for large \(h\) the corresponding distribution is concentrated on the constant plus-configuration. At the non-trivial critical point the magnetization jumps discontinuously. The authors discuss various non-Gibbsian properties of this state. The proofs are based on contour arguments and cluster expansions.