Journal of Statistical Physics

, Volume 21, Issue 5, pp 561–572

Zeros of the partition function and Gaussian inequalities for the plane rotator model

  • François Dunlop

DOI: 10.1007/BF01011168

Cite this article as:
Dunlop, F. J Stat Phys (1979) 21: 561. doi:10.1007/BF01011168


The partition function for ferromagnetic plane rotators in a complex external field μ, with ¦Im μ¦ ⩽ ¦Re μ ¦, is bounded below in modulus by its value at μ=0. The proof is based on complex combinations of duplicated variables which are positive definite on a subgroup of the configuration group. In the isotropic situation (and μ=0), the associated “Gaussian inequalities” imply that all truncated correlation functions decay at least as the two-point function.

Key words

Plane rotators Lee-Yang zeros Gaussian inequalities 

Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • François Dunlop
    • 1
  1. 1.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance

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