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

Abstract

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.

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Lebowitz, J.L., Mazel, A.E. A remark on the low-temperature behavior of the SOS interface in half-space. J Stat Phys 84, 379–397 (1996). https://doi.org/10.1007/BF02179648

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Key Words

  • Gibbs state
  • SOS model
  • layering transition
  • uniqueness
  • FKG
  • cluster expansion