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Gibbsianness and non-Gibbsianness in lattice random fields. (English) Zbl 1458.82009

Bovier, Anton (ed.) et al., Mathematical statistical physics. École d’Été de Physique des Houches session LXXXIII, ESF Summer school École thématique du CNRS, Les Houches, France, July 4–29, 2005. Amsterdam: Elsevier. 731-799 (2006).
From the text: The notion of Gibbs measure, or Gibbs random field, is the founding stone of mathematical statistical mechanics. Its formalization in the late sixties, due to [R. L. Dobrushin, Teor. Veroyatn. Primen. 13, 201–229 (1968; Zbl 0184.40403)], marked the beginning of two decades of intense activity that produced a rather complete theory which has been exploited in many areas of mathematical physics, probability, and stochastic processes, as well as for example in dynamical systems.
For the entire collection see [Zbl 1191.82003].

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
60G57 Random measures
60G60 Random fields
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B28 Renormalization group methods in equilibrium statistical mechanics
82-03 History of statistical mechanics

Citations:

Zbl 0184.40403
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