{
  "id": "1911.05964",
  "version": "v1",
  "published": "2019-11-14T06:59:48.000Z",
  "updated": "2019-11-14T06:59:48.000Z",
  "title": "Tricritical directed percolation with long-range interaction in one and two dimensions",
  "authors": [
    "Minjae Jo",
    "B. Kahng"
  ],
  "comment": "16 pages, 21 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Recently, the quantum contact process, in which branching and coagulation processes occur both coherently and incoherently, was theoretically and experimentally investigated in driven open quantum spin systems. In the semi-classical approach, the quantum coherence effect was regarded as a process in which two consecutive atoms are involved in the excitation of a neighboring atom from the inactive (ground) state to the active state (excited $s$ state). In this case, both second-order and first-order transitions occur. Therefore, a tricritical point exists at which the transition belongs to the tricritical directed percolation (TDP) class. On the other hand, when an atom is excited to the $d$ state, long-range interaction is induced. Here, to account for this long-range interaction, we extend the TDP model to one with long-range interaction in the form of $\\sim 1/r^{d+\\sigma}$ (denoted as LTDP), where $r$ is the separation, $d$ is the spatial dimension, and $\\sigma$ is a control parameter. In particular, we investigate the properties of the LTDP class below the upper critical dimension $d_c=$ min$(3,\\,1.5\\sigma)$. We numerically obtain a set of critical exponents in the LTDP class and determine the interval of $\\sigma$ for the LTDP class. Finally, we construct a diagram of universality classes in the space ($d$, $\\sigma$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-14T06:59:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long-range interaction",
      "tricritical directed percolation",
      "ltdp class",
      "driven open quantum spin systems",
      "coagulation processes occur"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}