{
  "id": "1611.04547",
  "version": "v1",
  "published": "2016-11-14T20:11:32.000Z",
  "updated": "2016-11-14T20:11:32.000Z",
  "title": "Phase transitions in long-range Ising models and an optimal condition for factors of $g$-measures",
  "authors": [
    "Anders Johansson",
    "Anders Öberg",
    "Mark Pollicott"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We weaken the assumption of summable variations in a paper by Verbitskiy \\cite{verb} to a weaker condition, Berbee's condition, in order for a 1-block factor (a single site renormalisation) of the full shift space on finitely many symbols to have a $g$-measure with a continuous $g$-function. But we also prove by means of a counterexample, that this condition is (within constants) optimal. The counterexample is based on the second of our main results, where we prove that there is an inverse critical temperature in a one-sided long-range Ising model which is at most 8 times the critical inverse temperature for the (two-sided) Ising model with long-range interactions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-14T20:11:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37A60",
      "82B20",
      "82B26"
    ],
    "keywords": [
      "phase transitions",
      "optimal condition",
      "single site renormalisation",
      "full shift space",
      "counterexample"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}