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Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability. (English) Zbl 1187.82076
One considers Glauber dynamics for the Ising model on sequences of transitive graphs. It is shown that the system exhibits a cut-off for values of the absolute temperature $$T$$ larger than the unity. When $$T=1$$, one can obtain the order $$n^{3/2}$$ of the mixing time, and the meta-stability of the system is analyzed when $$T$$ is small. In this case, it is shown that the mixing time is logarithmic

##### MSC:
 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60K35 Interacting random processes; statistical mechanics type models; percolation theory
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