{
  "id": "2407.21112",
  "version": "v1",
  "published": "2024-07-30T18:05:22.000Z",
  "updated": "2024-07-30T18:05:22.000Z",
  "title": "Exponential growth rate of lattice comb polymers",
  "authors": [
    "EJ Janse van Rensburg",
    "SG Whittington"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate a lattice model of comb polymers and derive bounds on the exponential growth rate of the number of embeddings of the comb. A comb is composed of a backbone that is a self-avoiding walk and a set of $t$ teeth, also modelled as mutually and self-avoiding walks, attached to the backbone at vertices or nodes of degree 3. Each tooth of the comb has $m_a$ edges and there are $m_b$ edges in the backbone between adjacent degree 3 vertices and between the first and last nodes of degree 3 and the end vertices of degree 1 of the backbone. We are interested in the exponential growth rate as $t \\to \\infty$ with $m_a$ and $m_b$ fixed. We prove upper bounds on this growth rate and show that for small values of $m_a$ the growth rate is strictly less than that of self-avoiding walks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-30T18:05:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B41",
      "82B80",
      "65C05"
    ],
    "keywords": [
      "exponential growth rate",
      "lattice comb polymers",
      "self-avoiding walk",
      "lattice model",
      "small values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}