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Annales Henri Poincaré

, Volume 1, Issue 1, pp 59–100 | Cite as

Correlation Asymptotics of Classical Lattice Spin Systems with Nonconvex Hamilton Function at Low Temperature

  • V. Bach
  • T. Jecko
  • J. Sjöstrand

Abstract.

The present paper continues Sjöstrand's study [14] of correlation functions of lattice field theories by means of Witten's deformed Laplacian. Under the assumptions specified in the paper and for sufficiently low temperature, we derive an estimate for the spectral gap of a certain Witten Laplacian which enables us to prove the exponential decay of the two-point correlation function and, further, to derive its asymptotics, as the distance between the spin sites becomes large. Typically, our assumptions do not require uniform strict convexity and apply to Hamiltonian functions which have a single, nondegenerate minimum and no other extremal point.

Keywords. Correlation Function, Lattice Spin Systems, Exponential Decay, Witten Laplacian. 

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Copyright information

© Birkhäuser Verlag Basel, 2000

Authors and Affiliations

  • V. Bach
    • 1
  • T. Jecko
    • 1
  • J. Sjöstrand
    • 2
  1. 1.FB Mathematik MA 7-2, TU Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany, e-mail: bach@math.tu-berlin.de and jecko@math.tu-berlin.deDE
  2. 2.Centre de Mathématiques, Ecole Polytechnique, CNRS, URA 169, F-91128 Palaiseau Cedex, France, e-mail: johannes@math.polytechnique.frFR

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