{
  "id": "1405.3309",
  "version": "v2",
  "published": "2014-05-13T21:20:53.000Z",
  "updated": "2015-03-05T00:11:13.000Z",
  "title": "The effect of quenched bond disorder on first-order phase transitions",
  "authors": [
    "Arash Bellafard",
    "Sudip Chakravarty",
    "Matthias Troyer",
    "Helmut G. Katzgraber"
  ],
  "comment": "8 pages, 11 figures; the simulations are now extended to 128x128 lattice with three colors of the Ashvin-Teller model",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "cond-mat.str-el"
  ],
  "abstract": "We investigate the effect of quenched bond disorder on the two-dimensional three-color Ashkin-Teller model, which undergoes a first-order phase transition in the absence of impurities. This is one of the simplest and striking models in which quantitative numerical simulations can be carried out to investigate emergent criticality due to disorder rounding of first-order transition. Utilizing extensive cluster Monte Carlo simulations on large lattice sizes of up to $128 \\times 128$ spins, each of which is represented by three colors taking values $\\pm 1$, we show that the rounding of the first-order phase transition is an emergent criticality. We further calculate the correlation length critical exponent, $\\nu$, and the magnetization critical exponent, $\\beta$, from finite size scaling analysis. We find that the critical exponents, $\\nu$ and $\\beta$, change as the strength of disorder or the four-spin coupling varies, and we show that the critical exponents appear not to be in the Ising universality class. We know of no analytical approaches that can explain our non-perturbative results. However our results should inspire further work on this important problem, either numerical or analytical.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-13T21:20:53.000Z",
      "abstract": "We investigate the effect of quenched bond disorder on the two-dimensional three-color Ashkin-Teller model, which undergoes a first-order phase transition in the absence of impurities. This is one of the simplest, but illuminating, model in which quantitative numerical simulations can be carried out. Utilizing extensive cluster Monte Carlo simulations on large lattice sizes of up to $96 \\times 96$, we show that the rounding of the first-order phase transition is an emergent criticality. We calculate the correlation length critical exponent, $\\nu$, and magnetization critical exponent, $\\beta$. We find that the critical exponents, $\\nu$ and $\\beta$, change as the strength of disorder or the four-spin coupling varies, and we show that the correlation length critical exponent violates the lower bound $2/D \\le \\nu$, where $D$ is the dimension of the system. Present results on much larger lattices up to $96\\times 96$ fully vindicates our earlier conclusions derived from smaller lattices up to $32\\times 32$. Recalling that the model involves three degrees of freedom at each site, it would probably be difficult to extend to even larger lattices, but given that the conclusions are unchanged gives us some confidence of the correctness of our work.",
      "comment": "7 pages, 9 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-05T00:11:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first-order phase transition",
      "quenched bond disorder",
      "cluster monte carlo simulations",
      "correlation length critical exponent",
      "extensive cluster monte carlo"
    ],
    "publication": {
      "doi": "10.1016/j.aop.2015.03.026",
      "journal": "Annals of Physics",
      "year": 2015,
      "month": "Jun",
      "volume": 357,
      "pages": 66
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015AnPhy.357...66B"
    }
  }
}