{
  "id": "cond-mat/0104135",
  "version": "v1",
  "published": "2001-04-09T02:15:42.000Z",
  "updated": "2001-04-09T02:15:42.000Z",
  "title": "Scaling of Self-Avoiding Walks in High Dimensions",
  "authors": [
    "Aleksander L. Owczarek",
    "Thomas Prellberg"
  ],
  "comment": "14 pages, 2 figures",
  "doi": "10.1088/0305-4470/34/29/303",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N=16384, providing the first such results in dimensions $d > 4$ on which we concentrate our analysis. We analyse the scaling behaviour of the partition function and the statistics of nearest-neighbour contacts, as well as the average geometric size of the walks, and compare our results to $1/d$-expansions and to excellent rigorous bounds that exist. In particular, we obtain precise values for the connective constants, $\\mu_5=8.838544(3)$, $\\mu_6=10.878094(4)$, $\\mu_7=12.902817(3)$, $\\mu_8=14.919257(2)$ and give a revised estimate of $\\mu_4=6.774043(5)$. All of these are by at least one order of magnitude more accurate than those previously given (from other approaches in $d>4$ and all approaches in $d=4$). Our results are consistent with most theoretical predictions, though in $d=5$ we find clear evidence of anomalous $N^{-1/2}$-corrections for the scaling of the geometric size of the walks, which we understand as a non-analytic correction to scaling of the general form $N^{(4-d)/2}$ (not present in pure Gaussian random walks).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-09T02:15:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-avoiding walks",
      "high dimensions",
      "pure gaussian random walks",
      "high-precision monte-carlo simulations",
      "general form"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}