{
  "id": "2410.11763",
  "version": "v1",
  "published": "2024-10-15T16:35:46.000Z",
  "updated": "2024-10-15T16:35:46.000Z",
  "title": "Partition function zeros of the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice",
  "authors": [
    "Denis Gessert",
    "Martin Weigel",
    "Wolfhard Janke"
  ],
  "comment": "31 pages, 7 figures",
  "categories": [
    "cond-mat.stat-mech",
    "physics.comp-ph"
  ],
  "abstract": "We study the zeros of the partition function in the complex temperature plane (Fisher zeros) and in the complex external field plane (Lee-Yang zeros) of a frustrated Ising model with competing nearest-neighbor ($J_1 > 0$) and next-nearest-neighbor ($J_2 < 0$) interactions on the honeycomb lattice. We consider the finite-size scaling (FSS) of the leading Fisher and Lee-Yang zeros as determined from a cumulant method and compare it to a traditional scaling analysis based on the logarithmic derivative of the magnetization $\\partial \\ln \\langle |M| \\rangle /\\partial\\beta$ and the magnetic susceptibility $\\chi$. While for this model both FSS approaches are subject to strong corrections to scaling induced by the frustration, their behavior is rather different, in particular as the ratio $\\mathcal{R} = J_2/J_1$ is varied. As a consequence, an analysis of the scaling of partition function zeros turns out to be a useful complement to a more traditional FSS analysis. For the cumulant method, we also study the convergence as a function of cumulant order, providing suggestions for practical implementations. The scaling of the zeros convincingly shows that the system remains in the Ising universality class for $\\mathcal{R}$ as low as $-0.22$, where results from traditional FSS using the same simulation data are less conclusive. The approach hence provides a valuable additional tool for mapping out the phase diagram of models afflicted by strong corrections to scaling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-15T16:35:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "honeycomb lattice",
      "ising model",
      "traditional fss",
      "partition function zeros turns",
      "strong corrections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}