{
  "id": "2311.18058",
  "version": "v1",
  "published": "2023-11-29T20:09:25.000Z",
  "updated": "2023-11-29T20:09:25.000Z",
  "title": "Phase Transitions in the semi-infinite Ising model with a decaying field",
  "authors": [
    "Rodrigo Bissacot",
    "João Maia"
  ],
  "comment": "16 pages, 6 figures",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We study the semi-infinite Ising model with an external field $h_i = \\lambda |i_d|^{-\\delta}$, $\\lambda$ is the wall influence, and $\\delta>0$. This external field decays as it gets further away from the wall. We are able to show that when $\\delta>1$ and $\\beta > \\beta_c(d)$, there exists a critical value $0< \\lambda_c:=\\lambda_c(\\delta,\\beta)$ such that, for $\\lambda<\\lambda_c$ there is phase transition and for $\\lambda>\\lambda_c$ we have uniqueness of the Gibbs state. In addition, when $\\delta<1$, we have only one Gibbs state for any positive $\\beta$ and $\\lambda$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-29T20:09:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B05",
      "82B20",
      "82B26"
    ],
    "keywords": [
      "semi-infinite ising model",
      "phase transition",
      "decaying field",
      "gibbs state",
      "external field decays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}