Communications in Mathematical Physics

, Volume 16, Issue 4, pp 310–328

General formulation of Griffiths' inequalities

  • J. Ginibre

DOI: 10.1007/BF01646537

Cite this article as:
Ginibre, J. Commun.Math. Phys. (1970) 16: 310. doi:10.1007/BF01646537


We present a general framework in which Griffiths inequalities on the correlations of ferromagnetic spin systems appear as natural consequences of general assumptions. We give a method for the construction of a large class of models satisfying the basic assumptions. Special cases include the Ising model with arbitrary spins, and the plane rotator model. The general theory extends in a straightforward way to the non-commutative (quantum) case, but non-commutative examples satisfying all the assumptions are lacking at the moment.

Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • J. Ginibre
    • 1
  1. 1.Laboratoire de Physique Théorique et Hautes Energies91-OrsayFrance

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