{
  "id": "1805.05725",
  "version": "v1",
  "published": "2018-05-15T12:20:45.000Z",
  "updated": "2018-05-15T12:20:45.000Z",
  "title": "Logarithm corrections in the critical behavior of the Ising model on a triangular lattice modulated with the Fibonacci sequence",
  "authors": [
    "T. F. A. Alves",
    "G. A. Alves",
    "M. S. Vasconcelos"
  ],
  "comment": "17 pages, 9 figures",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We investigated the critical behavior of the Ising model in a triangular lattice with ferro and anti-ferromagnetic interactions modulated by the Fibonacci sequence, by using finite-size numerical simulations. Specifically, we used a replica exchange Monte Carlo method, known as Parallel Tempering, to calculate the thermodynamic quantities of the system. We have obtained the staggered magnetization $q$, the associated magnetic susceptibility ($\\chi$) and the specific heat $c$, to characterize the universality class of the system. At the low-temperature limit, we have obtained a continuous phase transition with a critical temperature around $T_{c} \\approx 1.4116$ for a particular modulation of the lattice according to the Fibonacci letter sequence. In addition, we have used finite-size scaling relations with logarithmic corrections to estimate the critical exponents $\\beta$, $\\gamma$ and $\\nu$, and the correction exponents $\\hat{\\beta}$, $\\hat{\\gamma}$, $\\hat{\\alpha}$ and $\\hat{\\lambda}$. Our results show that the system obeys the Ising model universality class and that the critical behavior has logarithmic corrections.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-15T12:20:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical behavior",
      "ising model",
      "fibonacci sequence",
      "triangular lattice",
      "logarithm corrections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}