Communications in Mathematical Physics

, Volume 78, Issue 4, pp 545–566 | Cite as

Lattice systems with a continuous symmetry

III. Low temperature asymptotic expansion for the plane rotator model
  • Jean Bricmont
  • Jean-Raymond Fontaine
  • Joel L. Lebowitz
  • Elliott H. Lieb
  • Thomas Spencer
Article

Abstract

We prove that the expansion in powers of the temperatureT of the correlation functions and the free energy of the plane rotator model on ad-dimensional lattice is asymptotic to all orders inT. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures ford=3.

Keywords

Neural Network Free Energy Correlation Function High Power Nonlinear Dynamics 

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Jean Bricmont
    • 1
  • Jean-Raymond Fontaine
    • 2
  • Joel L. Lebowitz
    • 2
  • Elliott H. Lieb
    • 3
  • Thomas Spencer
    • 2
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsRutgers UniversityNew BrunswickUSA
  3. 3.Department of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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