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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

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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