Communications in Mathematical Physics

, Volume 73, Issue 1, pp 83–94

Translation invariance and instability of phase coexistence in the two dimensional Ising system

  • Michael Aizenman

DOI: 10.1007/BF01942696

Cite this article as:
Aizenman, M. Commun.Math. Phys. (1980) 73: 83. doi:10.1007/BF01942696


It is shown that any Gibbs state of the two dimensional ferromagnetic Ising system is of the form λμ++(1−λ)μ, with some λ∈ [0, 1]. This excludes the possibility of a locally stable phase coexistence and of translation symmetry breaking, which are known to occur in higher dimensions. Use is made in the proof of the stochastic aspects of the geometry of the interface lines.

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Michael Aizenman
    • 1
  1. 1.Department of PhysicsPrinceton UniversityPrincetonUSA