{
  "id": "0711.3445",
  "version": "v1",
  "published": "2007-11-21T20:19:12.000Z",
  "updated": "2007-11-21T20:19:12.000Z",
  "title": "Finite size corrections in the Sherrington-Kirkpatrick model",
  "authors": [
    "T. Aspelmeier",
    "A. Billoire",
    "E. Marinari",
    "M. A. Moore"
  ],
  "comment": "Contribution to the conference \"Viewing the World through Spin Glasses\" in honour of Professor David Sherrington on the occasion of his 65th birthday, 31 August - 1 September 2007",
  "journal": "J. Phys. A: Math. Theor. 41 (2008) 324008",
  "doi": "10.1088/1751-8113/41/32/324008",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We argue that when the number of spins $N$ in the SK model is finite, the Parisi scheme can be terminated after $K$ replica-symmetry breaking steps, where $K(N) \\propto N^{1/6}$. We have checked this idea by Monte Carlo simulations: we expect the typical number of peaks and features $R$ in the (non-bond averaged) Parisi overlap function $P_J(q)$ to be of order $2K(N)$, and our counting (for samples of size $N$ up to 4096 spins) gives results which are consistent with our arguments. We can estimate the leading finite size correction for any thermodynamic quantity by finding its $K$ dependence in the Parisi scheme and then replacing $K$ by K(N). Our predictions of how the Edwards-Anderson order parameter and the internal energy of the system approach their thermodynamic limit compare well with the results of our Monte Carlo simulations. The $N$-dependence of the sample-to-sample fluctuations of thermodynamic quantities can also be obtained; the total internal energy should have sample-to-sample fluctuations of order $N^{1/6}$, which is again consistent with the results of our numerical simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-21T20:19:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite size correction",
      "sherrington-kirkpatrick model",
      "monte carlo simulations",
      "sample-to-sample fluctuations",
      "parisi scheme"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2008,
      "month": "Aug",
      "volume": 41,
      "number": 32,
      "pages": 324008
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JPhA...41F4008A"
    }
  }
}