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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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