Mixing in Time and Space for Lattice Spin Systems: A Combinatorial View
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The paper considers spin systems on the d-dimensional integer lattice ℤd with nearest-neighbor interactions. A sharp equivalence is proved between exponential decay with distance of spin correlations (a spatial property of the equilibrium state) and “super-fast” mixing time of the Glauber dynamics (a temporal property of a Markov chain Monte Carlo algorithm). While such an equivalence is already known in various forms, the proofs in this paper are purely combinatorial and avoid the functional analysis machinery employed in previous proofs.
KeywordsSpin System Gibbs Measure Markov Chain Monte Carlo Algorithm Spin Space Gibbs Distribution
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