Journal of Statistical Physics

, Volume 84, Issue 3–4, pp 379–397 | Cite as

A remark on the low-temperature behavior of the SOS interface in half-space

  • J. L. Lebowitz
  • A. E. Mazel


We investigate the low-temperature phase diagram of thed-dimensional (d≥2) solid-on-solid (SOS) interface constrained to lie above a rigid wall to which it is attracted by a constant force. We prove uniqueness of the Gibbs state and exponentially fast convergence (in the diameter of the domain) of the finite-volume expectation of local observables, for all values of parameters where uniqueness in the class of translation-periodic limit Gibbs states was established previously. These domains of uniqueness are bordered by lines on which the system undergoes a layering transition.

Key Words

Gibbs state SOS model layering transition uniqueness FKG cluster expansion 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • J. L. Lebowitz
    • 1
  • A. E. Mazel
    • 1
    • 2
  1. 1.Department of Mathematics and PhysicsRutgers UniversityNew Brunswick
  2. 2.International Institute of Earthquake Prediction Theory and Mathematical GeophysicsRussian Academy of SciencesMoscowRussia

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