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Stochastic geometry in statistical mechanics and quantum field theory. (English) Zbl 0564.60012
Proc. Int. Congr. Math., Warszawa 1983, Vol. 2, 1297-1307 (1984).
[For the entire collection see Zbl 0553.00001.]
This is a short but well-organized review on the stochastic-geometric aspects of the critical behavior in statistical mechanical systems and in quantum fields. The main attention is paid to the existence of the ”upper-critical dimensions”, above which the critical behavior is quite simple, and below which it is rather non-trivial.
Reviewer: V.A.Zagrebnov

MSC:
60D05 Geometric probability and stochastic geometry
82B05 Classical equilibrium statistical mechanics (general)
82B26 Phase transitions (general) in equilibrium statistical mechanics
81T08 Constructive quantum field theory