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Mixing in Time and Space for Lattice Spin Systems: A Combinatorial View

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Book cover Randomization and Approximation Techniques in Computer Science (RANDOM 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2483))

Abstract

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.

Supported by EPSRC grant “Sharper Analysis of Randomised Algorithms: a ComputationalApproach” and by EC IST project RAND-APX.

Supported in part by NSF grants CCR-9820951 and CCR-0121555, and by DARPA cooperative agreement F30602-00-2-060.

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Author information

Authors and Affiliations

  1. School of Computing, University of Leeds, Leeds, LS2 9JT, UK

    Martin Dyer

  2. Computer Science Division, University of California at Berkeley, Berkeley, CA, 94720-1776, USA

    Alistair Sinclair & Dror Weitz

  3. Department of Computer Science, University of Chicago, Chicago, IL, 60637, USA

    Eric Vigoda

Authors
  1. Martin Dyer
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  2. Alistair Sinclair
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  3. Eric Vigoda
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  4. Dror Weitz
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Editor information

Editors and Affiliations

  1. Centre Universitaire d’Informatique, University of Geneva, 24, Rue Général Dufour, 1211, Genéve 4, Switzerland

    José D. P. Rolim

  2. Harvard University, DEAS, Maxwell Dworkin 337, 33 Oxford Street, Cambridge, MA, 02138, USA

    Salil Vadhan

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© 2002 Springer-Verlag Berlin Heidelberg

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Dyer, M., Sinclair, A., Vigoda, E., Weitz, D. (2002). Mixing in Time and Space for Lattice Spin Systems: A Combinatorial View. In: Rolim, J.D.P., Vadhan, S. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 2002. Lecture Notes in Computer Science, vol 2483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45726-7_13

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  • DOI: https://doi.org/10.1007/3-540-45726-7_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44147-2

  • Online ISBN: 978-3-540-45726-8

  • eBook Packages: Springer Book Archive

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