{
  "id": "2408.11702",
  "version": "v1",
  "published": "2024-08-21T15:27:12.000Z",
  "updated": "2024-08-21T15:27:12.000Z",
  "title": "Local order metrics for many-particle systems across length scales",
  "authors": [
    "Charles Emmett Maher",
    "Salvatore Torquato"
  ],
  "comment": "19 pages, 8 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in $d$-dimensional Euclidean space $\\mathbb{R}^d$ across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of $n$-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the number variance $\\sigma_N^2(R)$ associated with a spherical sampling window of radius $R$ (which encodes pair correlations) and an integral measure derived from it $\\Sigma_N(R_i,R_j)$ that depends on two specified radial distances $R_i$ and $R_j$. Across the first three space dimensions ($d = 1,2,3$), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale $R$. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of $R$. These order metrics could also aid in the inverse design of structures with prescribed scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments [S. Torquato et al., Phys. Rev. X, 11, 021028 (2021)] to devise even more sensitive order metrics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-21T15:27:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local order metrics",
      "length scale",
      "order/disorder",
      "particle correlation functions",
      "local variance metrics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}