{
  "id": "1510.07341",
  "version": "v1",
  "published": "2015-10-26T01:05:19.000Z",
  "updated": "2015-10-26T01:05:19.000Z",
  "title": "Microscopic theory of phase transitions in a critical region",
  "authors": [
    "Vitaly V. Kocharovsky",
    "Vladimir V. Kocharovsky"
  ],
  "comment": "23 pages",
  "journal": "Physica Scripta 90, 108002 (2015)",
  "doi": "10.1088/0031-8949/90/10/108002",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The problem of finding a microscopic theory of phase transitions across a critical point is a central unsolved problem in theoretical physics. We find a general solution to that problem and present it here for the cases of Bose-Einstein condensation in an interacting gas and ferromagnetism in a lattice of spins, interacting via a Heisenberg or Ising Hamiltonian. For Bose-Einstein condensation, we present the exact, valid for the entire critical region, equations for the Green functions and order parameter, that is a critical-region extension of the Beliaev-Popov and Gross-Pitaevskii equations. For the magnetic phase transition, we find an exact theory in terms of constrained bosons in a lattice and obtain similar equations for the Green functions and order parameter. In particular, we outline an exact solution for the three-dimensional Ising model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-26T01:05:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "microscopic theory",
      "order parameter",
      "bose-einstein condensation",
      "green functions",
      "magnetic phase transition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP",
      "journal": "Physica Scripta",
      "year": 2015,
      "month": "Oct",
      "volume": 90,
      "number": 10,
      "pages": 108002
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015PhyS...90j8002K"
    }
  }
}