{
  "id": "1803.04041",
  "version": "v1",
  "published": "2018-03-11T21:15:55.000Z",
  "updated": "2018-03-11T21:15:55.000Z",
  "title": "Hard-core configurations on a triangular lattice and Eisenstein primes",
  "authors": [
    "A. Mazel",
    "I. Stuhl",
    "Y. Suhov"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the Gibbs statistics of high-density hard-core random configurations on a triangular lattice. Depending on certain arithmetic properties of the repulsion diameter $D$ (related to Eisenstein integers), we identify, for a large fugacity, the extreme periodic Gibbs measures and analyze their properties. (a) For the values of $D$ belonging to certain arithmetic classes a complete phase diagram is established. (b) For the remaining values of $D$ we prove non-uniqueness of a pure phase and provide some additional information. We argue that in general the list of extreme periodic Gibbs measures can vary according to the arithmetic structure of $D$. This argument is supported by the analysis of several specific values of $D$ (outside the classes from (a)) for which the complete phase diagram is established, using in part a computer assistance. The proofs are achieved by applying Zahradnik's extension of the Pirogov--Sinai theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-11T21:15:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G60",
      "82B20"
    ],
    "keywords": [
      "triangular lattice",
      "eisenstein primes",
      "hard-core configurations",
      "extreme periodic gibbs measures",
      "complete phase diagram"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}