Lattice systems with a continuous symmetry - II. Decay of correlations

Jean Bricmont, Jean Raymond Fontaine, Joel L. Lebowitz, Thomas Spencer

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18 Scopus citations

Abstract

We consider perturbations of a massless Gaussian lattice field on ℤd, d≧3, which preserves the continuous symmetry of the Hamiltonian, e.g., {Mathematical expression} It is known that for all T>0 the correlation functions in this model do not decay exponentially. We derive a power law upper bound for all (truncated) correlation functions. Our method is based on a combination of the log concavity inequalities of Brascamp and Lieb, reflection positivity and the Fortuin, Kasteleyn and Ginibre (F.K.G.) inequalities.

Original languageEnglish (US)
Pages (from-to)363-371
Number of pages9
JournalCommunications In Mathematical Physics
Volume78
Issue number3
DOIs
StatePublished - Jan 1981

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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