Communications in Mathematical Physics

, Volume 66, Issue 1, pp 1–20 | Cite as

Non-translation invariant Gibbs states with coexisting phases

I. Existence of sharp interface for Widom-Rowlinson type lattice models in three dimensions
  • Jean Bricmont
  • Joel L. Lebowitz
  • Charles E. Pfister
  • Enzo Olivieri


We investigate the spatially inhomogeneous states of two component,A - B, Widom-Rowlinson type lattice systems. When the fugacity of the two components are equal and large, these systems can exist in two different homogeneous (translation invariant) pure phases oneA-rich and oneB-rich. We consider now the system in a box with boundaries favoring the segregation of these two phases into “top and bottom” parts of the box. Utilizing methods due to Dobrushin we prove the existence, in three or more dimensions, of a “sharp” interface for the system which persists in the limit of the size of the box going to infinity. We also give some background on rigorous results for the interface problem in Ising spin systems.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Jean Bricmont
    • 1
  • Joel L. Lebowitz
    • 1
  • Charles E. Pfister
    • 1
  • Enzo Olivieri
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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