Abstract.
We consider the low temperature Ising model in a uniform magnetic field h > 0 with minus boundary conditions and conditioned on having no internal contours. This simple contour model defines a non-Gibbsian spin state. For large enough magnetic fields (h >: h c ) this state is concentrated on the single spin configuration of all spins up. For smaller values (h≤h c ), the spin state is non-trivial. At the critical point h c ≠ 0 the magnetization jumps discontinuously. Freezing provides also an example of a translation invariant weakly Gibbsian state which is not almost Gibbsian.
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Received: 10 November 1998
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Maes, C., Shlosman, S. Freezing transition in the Ising model without internal contours. Probab Theory Relat Fields 115, 479–503 (1999). https://doi.org/10.1007/s004400050246
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DOI: https://doi.org/10.1007/s004400050246