Freezing transition in the Ising model without internal contours

Christian Maes, Senya Shlosman

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 > hc) this state is concentrated on the single spin configuration of all spins up. For smaller values (h ≤ hc), the spin state is non-trivial. At the critical point hc ≠ 0 the magnetization jumps discontinuously. Freezing provides also an example of a translation invariant weakly Gibbsian state which is not almost Gibbsian.

Original languageEnglish
Pages (from-to)479-503
Number of pages25
JournalProbability Theory and Related Fields
Issue number4
Publication statusPublished - Dec 1999
Externally publishedYes


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