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Mixing time for the Ising model: a uniform lower bound for all graphs. (English. French summary) Zbl 1274.82012
The authors provide the strict mathematical analysis of the Ising model on a finite graph \(G=(V,E)\) with the interaction strength \(J\) defined by the probability measure \( \mu_G(\sigma)=Z^{-1}\exp\left(\Sigma_{u,v}J_{u,v}\sigma(u)\sigma(v)\right), \sigma\in\Omega,u,v\in E \) on the configuration space \(\Omega=\{\pm1\}^V\). The theorem, which states that the spin mixing time of Glauber dynamics has the infimum \((1/4+o(1))n\log n\) over all \(n\)-vertex graphs \(G\) and all non-negative interaction matrices \(J\), is proven.

MSC:
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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