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Finitary coding for the sub-critical Ising model with finite expected coding volume. (English) Zbl 1441.60088

Summary: It has been shown by J. van den Berg and J. E. Steif [Ann. Probab. 27, No. 3, 1501–1522 (1999; Zbl 0968.60091)] that the sub-critical Ising model on \(\mathbb{Z}^d\) is a finitary factor of a finite-valued i.i.d. process. We strengthen this by showing that the factor map can be made to have finite expected coding volume (in fact, stretched-exponential tails), answering a question of van den Berg and Steif. The result holds at any temperature above the critical temperature. An analogous result holds for Markov random fields satisfying a high-noise assumption and for proper colorings with a large number of colors.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B26 Phase transitions (general) in equilibrium statistical mechanics
37A60 Dynamical aspects of statistical mechanics

Citations:

Zbl 0968.60091
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References:

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