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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Abstract

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
Volume350
Issue number13-14
DOIs
StatePublished - Jul 1 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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    Caputo, P., Lubetzky, E., Martinelli, F., Sly, A., & Toninelli, F. L. (2012). The shape of the (2+1)d SOS surface above a wall. Comptes Rendus Mathematique, 350(13-14), 703-706. https://doi.org/10.1016/j.crma.2012.07.006