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Long-time fluctuations of weakly interacting diffusions. (English) Zbl 0627.60105

Stochastic differential systems, Proc. IFIP-WG 7/1 Work. Conf., Eisenach/GDR 1986, Lect. Notes Control Inf. Sci. 96, 3-10 (1987).
[For the entire collection see Zbl 0619.00019.]
It is well-known that the ferromagnetic Ising model on the lattice \({\mathbb{Z}}^ 2\) with spins \(x_ k\in \{-1,+1\}\) and formal Hamiltonian \(H(x)=\sum_{| k-1| =1}| x_ k-x_ 1|^ 2\) exhibits a phase transition. In the low temperature region there exist two pure phases (i.e. two ergodic Gibbs distributions) having negative and positive mean magnetization, respectively.
The understanding of such dynamical phase transitions (sometimes called tunelling) and their mathematically rigorous investigation is a challenging problem. For models with short-range interaction such as the Ising model this seems to be a difficult task. One therefore tries to understand several aspects of the tunelling mechanism by investigating simpler models. (From the introduction.)
Reviewer: U.F.Wodarzik

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics

Citations:

Zbl 0619.00019