{
  "id": "2406.12040",
  "version": "v1",
  "published": "2024-06-17T19:19:50.000Z",
  "updated": "2024-06-17T19:19:50.000Z",
  "title": "Critical wetting in the (2+1)D Solid-On-Solid model",
  "authors": [
    "Joseph Chen",
    "Reza Gheissari",
    "Eyal Lubetzky"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this note, we study the low temperature $(2+1)$D SOS interface above a hard floor with critical pinning potential $\\lambda_w= \\log (\\frac{1}{1-e^{-4\\beta}})$. At $\\lambda<\\lambda_w$ entropic repulsion causes the surface to delocalize and be rigid at height $\\frac1{4\\beta}\\log n+O(1)$; at $\\lambda>\\lambda_w$ it is localized at some $O(1)$ height. We show that at $\\lambda=\\lambda_w$, there is delocalization, with rigidity now at height $\\lfloor \\frac1{6\\beta}\\log n+\\frac13\\rfloor$, confirming a conjecture of Lacoin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-17T19:19:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B20",
      "82B27"
    ],
    "keywords": [
      "solid-on-solid model",
      "critical wetting",
      "entropic repulsion",
      "hard floor",
      "low temperature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}