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Decay to equilibrium in random spin systems on a lattice. (English) Zbl 0882.60093

The authors prove for some continuous and discrete spin systems on \(\mathbb{Z}^d\) with random interactions, that there is no spectral gap at high temperature. In the 2-dimensional case they derive under certain assumptions on the random interaction an almost sure stretched exponential upper bound for the decay to equilibrium. The proofs are based on an approximation by finite-volume stochastic dynamics and the use of the logarithmic Sobolev inequality. The paper extends the results of the second author [J. Stat. Phys. 77, No. 3/4, 717-732 (1994; Zbl 0839.60102)].

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics

Citations:

Zbl 0839.60102
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References:

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