Journal of Statistical Physics

, Volume 26, Issue 2, pp 313–332 | Cite as

On the local structure of the phase separation line in the two-dimensional Ising system

  • J. Bricmont
  • J. L. Lebowitz
  • C. E. Pfister


We investigate the structure of the phase separation line between the pure phases in the two-dimensional Ising model, the liquid and vapor phase in lattice gas language, at low temperatures. The fluctuations in the location of this line are known to diverge in the thermodynamic limit, something which is also believed to happen to the continuum liquid-vapor interface in three dimensions (in the absence of the gravitational field). We show that despite this global divergence it is possible to define precisely the local structure of the phase separation line. This has a finite, exponentially small, width at low temperatures which is related by a central limit theorem(1) to the width of the global fluctuations on the appropriate (divergent) length scale. The latter has been computed explicitly(2) for all temperatures below the critical temperatureTc, where it diverges as (T c T)−1/2. We also prove a Gibbs formula for the surface tension at low temperature, which relates it to the local structure of the phase separation line.

Key words

Phase separation two-dimensional Ising model surface tension 


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Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • J. Bricmont
    • 1
  • J. L. Lebowitz
    • 2
  • C. E. Pfister
    • 3
  1. 1.Department of MathematicsPrinceton UniversityPrinceton
  2. 2.I.H.E.S.Bures-sur-YvetteFrance
  3. 3.Departement de MathematiquesEcole Polytechnique FédéraleLausanneSwitzerland

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