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Approach to equilibrium of Glauber dynamics in the one phase region. II: The general case. (English) Zbl 0793.60111

Summary: We develop a new method, based on renormalization group ideas (block decimation procedure), to prove, under an assumption of strong mixing in a finite cube \(\Lambda_ 0\), a logarithmic Sobolev inequality for the Gibbs state of a discrete spin system. As a consequence we derive the hypercontractivity of the Markov semigroup of the associated Glauber dynamics and the exponential convergence to equilibrium in the uniform norm in all volumes \(\Lambda\) “multiples” of the cube \(\Lambda_ 0\).
For part I see Zbl 0793.60110.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)

Citations:

Zbl 0793.60110
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References:

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