{
  "id": "2307.15022",
  "version": "v1",
  "published": "2023-07-27T17:26:00.000Z",
  "updated": "2023-07-27T17:26:00.000Z",
  "title": "A unified picture of continuous variation of critical exponents",
  "authors": [
    "Indranil Mukherjee",
    "P. K. Mohanty"
  ],
  "comment": "8 pages, 6 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Renormalization group (RG) theory allows continuous variation of critical exponents along a marginal direction (if any) but does not predict the functional form. Recently it was proposed that continuous variation must occur in a way that leaves scaling relations invariant. For magnetic phase transition, the variation can occur in three different ways: I. $\\gamma$ varies keeping $\\delta$ fixed, II. $\\delta$ varies keeping $\\gamma$ fixed and III. both $\\delta$ and $\\gamma$ vary. In this article, we study the isotropic Ashkin Teller model on a two-dimensional square lattice and show that the magnetic and electric phase transition along the self-dual line exhibit continuous variation of critical exponents which are of Type-I (formally known as weak universality) and Type-III respectively. We show that the scaling functions of both electric and magnetic phase transition are only a scaled version of the universal scaling function of the Ising universality class in two dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-27T17:26:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous variation",
      "critical exponents",
      "unified picture",
      "magnetic phase transition",
      "isotropic ashkin teller model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}