The shape of the (2+1)d SOS surface above a wall

Pietro Caputo, Eyal Lubetzky, Fabio Martinelli, Allan Sly, Fabio Lucio Toninelli

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9 Scopus citations


We give a full description for the shape of the classical (2+1)d Solid-On-Solid model above a wall, introduced by Temperley (1952) [14]. On an L×L box at a large inverse-temperature β the height of most sites concentrates on a single level h=[14βlogL] for most values of L. For a sequence of diverging boxes the ensemble of level lines of heights (h, h-1,...) has a scaling limit in Hausdorff distance iff the fractional parts of 14βlogL converge to a noncritical value. The scaling limit is explicitly given by nested distinct loops formed via translates of Wulff shapes. Finally, the h-level lines feature L 1/3+o(1) fluctuations from the side boundaries.

Original languageEnglish (US)
Pages (from-to)703-706
Number of pages4
JournalComptes Rendus Mathematique
Issue number13-14
StatePublished - Jul 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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