{
  "id": "1011.2256",
  "version": "v1",
  "published": "2010-11-10T01:51:12.000Z",
  "updated": "2010-11-10T01:51:12.000Z",
  "title": "On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three",
  "authors": [
    "Luigi Accardi",
    "Farrukh Mukhamedov",
    "Mansoor Saburov"
  ],
  "comment": "34 pages, 1 figure",
  "journal": "Ann. Henri Poincar\\'e 12 (2011), 1109--1144",
  "doi": "10.1007/s00023-011-0107-2",
  "categories": [
    "math-ph",
    "math.DS",
    "math.FA",
    "math.MP",
    "math.OA",
    "quant-ph"
  ],
  "abstract": "In the present paper we study forward Quantum Markov Chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY-model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two now quasi equivalent QMC for the given family of interaction operators $\\{K_{<x,y>}\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-10T01:51:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L53",
      "60J99",
      "46L60",
      "60G50",
      "82B10",
      "81Q10",
      "94A17"
    ],
    "keywords": [
      "cayley tree",
      "phase transition",
      "associated chain",
      "study forward quantum markov chains",
      "quasi equivalent qmc"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011AnHP...12.1109A"
    }
  }
}