Communications in Mathematical Physics

, Volume 86, Issue 1, pp 87–110 | Cite as

Borel summability of the 1/N expansion for theN-vector [O(N) non-linear σ] models

  • J. Fröhlich
  • A. Mardin
  • V. Rivasseau


We construct an analytic interpolation in 1/N for theN-vector [O(N) non-linear σ] models withN-component fields on a lattice. This interpolation, valid at sufficiently high temperatures, extends over a large domain in the complex plane containing the half plane Re(1/N)>0. We use this result to show that the 1/N expansion of the free energy density and of the correlation functions is Borel summable in the thermodynamic limit and at high temperature.


Neural Network Free Energy Statistical Physic Energy Density Correlation Function 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • J. Fröhlich
    • 1
  • A. Mardin
    • 2
  • V. Rivasseau
    • 3
  1. 1.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance
  2. 2.C.P.T., Ecole PolytechniquePalaiseau CédexFrance
  3. 3.The Institute for Advanced StudyPrincetonUSA

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