"Non-Gibbsian" states and their Gibbs description

R. L. Dobrushin, S. B. Shlosman

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


The driving principle behind this paper is the following thesis: "Every physically reasonable random field has to be a Gibbs random field". In this paper the so-called "non-Gibbsian" random fields are considered. The usual definition of the Gibbs field is generalized in such a way so as to include some of the discovered "non-Gibbsian" fields. The new definition is then used to show that the projection of the two-dimensional Ising model onto the one-dimensional sublattice ℤ1 falls into the class of the generalized Gibbs fields.

Original languageEnglish
Pages (from-to)125-179
Number of pages55
JournalCommunications in Mathematical Physics
Issue number1
Publication statusPublished - 1999
Externally publishedYes


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