{
  "id": "2409.07744",
  "version": "v1",
  "published": "2024-09-12T04:34:08.000Z",
  "updated": "2024-09-12T04:34:08.000Z",
  "title": "A numerical study of the zeroes of the grand partition function of hard needles of length $k$ on stripes of width $k$",
  "authors": [
    "Soumyadeep Sarma"
  ],
  "comment": "12 pages, 13 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We numerically study zeroes of the partition function for trimers ($k = 3$) on $3 \\times L$ strip. While such results for dimers ($k = 2$) on 2D lattices are well known to always lie on the negative real axis and are unbounded, here we see that the zeroes are bounded on branches in a finite-sized region and with a considerable number of them being complex. We analyze this result further to numerically study the density of zeroes on such branches, estimating the critical power-law exponents, and make interesting observations on density of filled sites in the lattice as a function of activity $z$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-12T04:34:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grand partition function",
      "hard needles",
      "numerical study",
      "2d lattices",
      "numerically study zeroes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}