### 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 language | English (US) |
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Pages (from-to) | 703-706 |

Number of pages | 4 |

Journal | Comptes Rendus Mathematique |

Volume | 350 |

Issue number | 13-14 |

DOIs | |

State | Published - Jul 1 2012 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

*Comptes Rendus Mathematique*,

*350*(13-14), 703-706. https://doi.org/10.1016/j.crma.2012.07.006