{
  "id": "cond-mat/0410031",
  "version": "v2",
  "published": "2004-10-01T15:11:16.000Z",
  "updated": "2004-10-11T16:28:09.000Z",
  "title": "Persistence in systems with conserved order parameter",
  "authors": [
    "P. Gonos",
    "A. J. Bray"
  ],
  "comment": "9 pages, minor revisions",
  "journal": "J. Phys. A 38, 1427 (2005)",
  "doi": "10.1088/0305-4470/38/7/002",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider the low-temperature coarsening dynamics of a one-dimensional Ising ferromagnet with conserved Kawasaki-like dynamics in the domain representation. Domains diffuse with size-dependent diffusion constant, $D(l) \\propto l^\\gamma$ with $\\gamma = -1$. We generalize this model to arbitrary $\\gamma$, and derive an expression for the domain density, $N(t) \\sim t^{-\\phi}$ with $\\phi=1/(2-\\gamma)$, using a scaling argument. We also investigate numerically the persistence exponent $\\theta$ characterizing the power-law decay of the number, $N_p(t)$, of persistent (unflipped) spins at time $t$, and find $N_{p}(t)\\sim t^{-\\theta}$ where $\\theta$ depends on $\\gamma$. We show how the results for $\\phi$ and $\\theta$ are related to similar calculations in diffusion-limited cluster-cluster aggregation (DLCA) where clusters with size-dependent diffusion constant diffuse through an immobile `empty' phase and aggregate irreversibly on impact. Simulations show that, while $\\phi$ is the same in both models, $\\theta$ is different except for $\\gamma=0$. We also investigate models that interpolate between symmetric domain diffusion and DLCA.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-10-11T16:28:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conserved order parameter",
      "persistence",
      "size-dependent diffusion constant diffuse",
      "symmetric domain diffusion",
      "domain representation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}