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Multiple critical behavior of probabilistic limit theorems in the neighborhood of a tricritical point. (English) Zbl 1156.82006

The Blume-Emery-Griffiths model is an important lattice-spin model (BEG model) which applies to a broad class of physical systems, and here, one considers a mean-field (or molecular field) version of this approach, and more especially one investigates the critical behaviour of some corresponding probabilistic theorems which involve scaling limits and moderate deviation principles (MDP) for the total spin (in the BEG model). The key of this unified approach is the use of a (magic) function \(G_{\beta,K}\) of which the global minimum points coincide with the set of equilibrium macrostates of the BEG model. One so arrives at 18 scaling limits and 18 MDPs, what illustrates the intricacy of the system.

MSC:

82B27 Critical phenomena in equilibrium statistical mechanics
82B26 Phase transitions (general) in equilibrium statistical mechanics
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