Communications in Mathematical Physics

, Volume 14, Issue 3, pp 205–234

Existence of phase transitions for quantum lattice systems

  • J. Ginibre

DOI: 10.1007/BF01645421

Cite this article as:
Ginibre, J. Commun.Math. Phys. (1969) 14: 205. doi:10.1007/BF01645421


We prove that the following lattice systems:
  1. (1)

    anisotropic Heisenberg model,

  2. (2)

    Ising model with transverse magnetic field,

  3. (3)

    quantum lattice gas with hard cores extending over nearest neighbours,

exhibit phase transitions if the temperature is sufficiently low and the transverse (or kinetic) part of the interaction sufficiently small.

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • J. Ginibre
    • 1
  1. 1.Laboratoire de Physique Théorique et Hautes EnergiesOrsayFrance

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