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Homogeneous nucleation for Glauber and Kawasaki dynamics in large volumes at low temperatures. (English) Zbl 1193.60114
The paper investigates the meta-stability in large volumes at low temperatures for Ising spins subject to Glauber’s spin-flip dynamics on the one hand; and for lattice gas particles subject to Kawasaki’s hopping dynamics, on the other hand. By using a suitable generalization of the potential-theoretic approach to meta-stability, one can so extend to large volumes some results which have been already obtained for small volumes. The main mathematical tools so involved are the Dirichlet problems associated with the dynamics, the definition of the Green function in terms of capacities and equilibrium potentials, and variational principles applied to these capacities. The problem is considered for both the Glauber’s and the Kawasaki’s dynamics; but it is much more difficult in the later case as a result of the fact that the corresponding dynamics is conservative.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
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