{
  "id": "cond-mat/0210036",
  "version": "v1",
  "published": "2002-10-01T22:36:39.000Z",
  "updated": "2002-10-01T22:36:39.000Z",
  "title": "Phase diagram of a probabilistic cellular automaton with three-site interactions",
  "authors": [
    "A. P. F. Atman",
    "R. Dickman",
    "J. G. Moreira"
  ],
  "comment": "15 pages, 7 figures, submited to PRE",
  "doi": "10.1103/PhysRevE.67.016107",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study a (1+1) dimensional probabilistic cellular automaton that is closely related to the Domany-Kinzel (DKCA), but in which the update of a given site depends on the state of {\\it three} sites at the previous time step. Thus, compared with the DKCA, there is an additional parameter, $p_3$, representing the probability for a site to be active at time $t$, given that its nearest neighbors and itself were active at time $t-1$. We study phase transitions and critical behavior for the activity {\\it and} for damage spreading, using one- and two-site mean-field approximations, and simulations, for $p_3=0$ and $p_3=1$. We find evidence for a line of tricritical points in the ($p_1, p_2, p_3$) parameter space, obtained using a mean-field approximation at pair level. To construct the phase diagram in simulations we employ the growth-exponent method in an interface representation. For $p_3 =0$, the phase diagram is similar to the DKCA, but the damage spreading transition exhibits a reentrant phase. For $p_3=1$, the growth-exponent method reproduces the two absorbing states, first and second-order phase transitions, bicritical point, and damage spreading transition recently identified by Bagnoli {\\it et al.} [Phys. Rev. E{\\bf 63}, 046116 (2001)].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-01T22:36:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "phase diagram",
      "three-site interactions",
      "damage spreading transition",
      "dimensional probabilistic cellular automaton",
      "growth-exponent method reproduces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}