{
  "id": "0710.1509",
  "version": "v1",
  "published": "2007-10-08T10:59:16.000Z",
  "updated": "2007-10-08T10:59:16.000Z",
  "title": "Asymptotic Behavior of Inflated Lattice Polygons",
  "authors": [
    "Mithun K. Mitra",
    "Gautam I. Menon",
    "R. Rajesh"
  ],
  "comment": "7 pages",
  "journal": "J. Stat. Phys. Vol 131, pg 393 (2008).",
  "doi": "10.1007/s10955-008-9512-4",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the inflated phase of two dimensional lattice polygons with fixed perimeter $N$ and variable area, associating a weight $\\exp[pA - Jb ]$ to a polygon with area $A$ and $b$ bends. For convex and column-convex polygons, we show that $<A >/A_{max} = 1 - K(J)/\\tilde{p}^2 + \\mathcal{O}(\\rho^{-\\tilde{p}})$, where $\\tilde{p}=pN \\gg 1$, and $\\rho<1$. The constant $K(J)$ is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for $J \\neq 0$. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-08T10:59:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic behavior",
      "inflated lattice polygons",
      "monte carlo simulations",
      "dimensional lattice polygons",
      "exact enumeration data"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2008,
      "month": "May",
      "volume": 131,
      "number": 3,
      "pages": 393
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JSP...131..393M"
    }
  }
}