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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)
##### Keywords:
Galuber dynamics; mixing time; Ising model
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##### References:
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