DOI: 10.1063/1.1338506. Precise determination of the critical percolation threshold for the three-dimensional “Swiss cheese” model using a growth algorithm

Precise determination of the critical percolation threshold for the three-dimensional “Swiss cheese” model using a growth algorithm

10.1063/1.1338506

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Precise values for the critical threshold for the three-dimensional “Swiss cheese” continuum percolation model have been calculated using extensive Monte Carlo simulations. These simulations used a growth algorithm and memory blocking scheme similar to what we used previously in three-dimensional lattice percolation. The simulations yield a value for the critical number density nc=0.652 960±0.000 005, which confirms recent work but extends the precision by two significant figures.

Bibliography

Lorenz, C. D., & Ziff, R. M. (2001). Precise determination of the critical percolation threshold for the three-dimensional âSwiss cheeseâ model using a growth algorithm. The Journal of Chemical Physics, 114(8), 3659â3661.

Authors 2

Christian D. Lorenz (first)
Robert M. Ziff (additional)

References 43 Referenced 191

10.1103/PhysRevB.28.3799 / Phys. Rev. B (1983)
10.1016/0266-3538(96)00054-1 / Comp. Sci. Technol. (1996)
10.1103/PhysRevLett.52.1465 / Phys. Rev. Lett. (1984)
10.1016/S0927-7757(99)00417-3 / Colloids Surf., A (2000)
10.1103/PhysRevA.34.3356 / Phys. Rev. A (1986)
10.1103/PhysRevA.35.5174 / Phys. Rev. A (1987)
10.1103/PhysRevB.42.4877 / Phys. Rev. B (1990)
10.1103/PhysRevB.35.197 / Phys. Rev. B (1987)
10.1063/1.478977 / J. Chem. Phys. (1999)
10.1063/1.479890 / J. Chem. Phys. (1999)
10.1063/1.473004 / J. Chem. Phys. (1996)
10.1063/1.454720 / J. Chem. Phys. (1988)
10.1103/PhysRevE.54.5331 / Phys. Rev. E (1996)
10.1103/PhysRevA.31.1222 / Phys. Rev. A (1985)
{'key': '2024021016532343900_r15', 'first-page': '5002', 'volume': '61', 'year': '2000', 'journal-title': 'Phys. Rev. E'} / Phys. Rev. E (2000)
10.1088/0305-4470/26/18/032 / J. Phys. A (1993)
10.1103/PhysRevB.37.2391 / Phys. Rev. B (1988)
10.1142/S0217984999000737 / Mod. Phys. Lett. B (1999)
10.1103/PhysRevA.41.5338 / Phys. Rev. A (1990)
{'key': '2024021016532343900_r20', 'first-page': 'L3991', 'volume': '33', 'year': '2000', 'journal-title': 'J. Phys. A'} / J. Phys. A (2000)
10.1088/0305-4470/30/16/005 / J. Phys. A (1997)
10.1088/0305-4470/14/8/007 / J. Phys. A (1981)
10.1088/0305-4470/22/4/004 / J. Phys. A (1989)
10.1103/PhysRevB.9.770 / Phys. Rev. B (1974)
10.1103/PhysRevLett.57.3195 / Phys. Rev. Lett. (1986)
10.1093/biomet/55.1.258 / Biometrika (1968)
10.1093/biomet/59.1.209 / Biometrika (1972)
10.1093/biomet/59.1.207 / Biometrika (1972)
10.1103/PhysRevB.10.1421 / Phys. Rev. B (1974)
10.1051/jphys:01974003505039300 / J. Phys. (Paris) (1974)
10.1051/jphys:01976003707-8081300 / J. Phys. (Paris) (1976)
10.1088/0305-4470/10/9/013 / J. Phys. A (1977)
10.1063/1.456595 / J. Chem. Phys. (1989)
10.1063/1.460401 / J. Chem. Phys. (1991)
{'key': '2024021016532343900_r35', 'first-page': '230', 'volume': '57', 'year': '1998', 'journal-title': 'Phys. Rev. E'} / Phys. Rev. E (1998)
10.1088/0305-4470/31/40/009 / J. Phys. A (1998)
10.1023/A:1018648130343 / J. Stat. Phys. (2000)
{'key': '2024021016532343900_r38'}
10.1088/0305-4470/17/15/018 / J. Phys. A (1984)
10.1088/0305-4470/30/15/021 / J. Phys. A (1997)
{'key': '2024021016532343900_r41'}
{'key': '2024021016532343900_r42'}
10.1088/0305-4470/32/1/004 / J. Phys. A (1999)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 10:14 a.m.)
Deposited	1 year, 6 months ago (Feb. 10, 2024, 12:43 p.m.)
Indexed	1 week ago (Aug. 26, 2025, 2:24 a.m.)
Issued	24 years, 6 months ago (Feb. 22, 2001)
Published	24 years, 6 months ago (Feb. 22, 2001)
Published Print	24 years, 6 months ago (Feb. 22, 2001)

Funders 0

None

BibTeX

@article{Lorenz_2001, title={Precise determination of the critical percolation threshold for the three-dimensional “Swiss cheese” model using a growth algorithm}, volume={114}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1338506}, DOI={10.1063/1.1338506}, number={8}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Lorenz, Christian D. and Ziff, Robert M.}, year={2001}, month=feb, pages={3659–3661} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        26
      ]
    ],
    "date-time": "2025-08-26T06:24:07Z",
    "timestamp": 1756189447384
  },
  "reference-count": 43,
  "publisher": "AIP Publishing",
  "issue": "8",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2001,
        2,
        22
      ]
    ]
  },
  "abstract": "<jats:p>Precise values for the critical threshold for the three-dimensional \u201cSwiss cheese\u201d continuum percolation model have been calculated using extensive Monte Carlo simulations. These simulations used a growth algorithm and memory blocking scheme similar to what we used previously in three-dimensional lattice percolation. The simulations yield a value for the critical number density nc=0.652\u200a960\u00b10.000\u200a005, which confirms recent work but extends the precision by two significant figures.</jats:p>",
  "DOI": "10.1063/1.1338506",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        26
      ]
    ],
    "date-time": "2002-07-26T14:14:42Z",
    "timestamp": 1027692882000
  },
  "page": "3659-3661",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 191,
  "title": "Precise determination of the critical percolation threshold for the three-dimensional \u201cSwiss cheese\u201d model using a growth algorithm",
  "prefix": "10.1063",
  "volume": "114",
  "author": [
    {
      "given": "Christian D.",
      "family": "Lorenz",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan\u200948109-2136"
        }
      ]
    },
    {
      "given": "Robert M.",
      "family": "Ziff",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan\u200948109-2136"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024021016532343900_r1",
      "doi-asserted-by": "crossref",
      "first-page": "3799",
      "DOI": "10.1103/PhysRevB.28.3799",
      "volume": "28",
      "year": "1983",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024021016532343900_r2",
      "doi-asserted-by": "crossref",
      "first-page": "911",
      "DOI": "10.1016/0266-3538(96)00054-1",
      "volume": "56",
      "year": "1996",
      "journal-title": "Comp. Sci. Technol."
    },
    {
      "key": "2024021016532343900_r3",
      "doi-asserted-by": "crossref",
      "first-page": "1465",
      "DOI": "10.1103/PhysRevLett.52.1465",
      "volume": "52",
      "year": "1984",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021016532343900_r4",
      "doi-asserted-by": "crossref",
      "first-page": "209",
      "DOI": "10.1016/S0927-7757(99)00417-3",
      "volume": "165",
      "year": "2000",
      "journal-title": "Colloids Surf., A"
    },
    {
      "key": "2024021016532343900_r5",
      "doi-asserted-by": "crossref",
      "first-page": "3356",
      "DOI": "10.1103/PhysRevA.34.3356",
      "volume": "34",
      "year": "1986",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024021016532343900_r6",
      "doi-asserted-by": "crossref",
      "first-page": "5174",
      "DOI": "10.1103/PhysRevA.35.5174",
      "volume": "35",
      "year": "1987",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024021016532343900_r7",
      "doi-asserted-by": "crossref",
      "first-page": "4877",
      "DOI": "10.1103/PhysRevB.42.4877",
      "volume": "42",
      "year": "1990",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024021016532343900_r8",
      "doi-asserted-by": "crossref",
      "first-page": "197",
      "DOI": "10.1103/PhysRevB.35.197",
      "volume": "35",
      "year": "1987",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024021016532343900_r9",
      "doi-asserted-by": "crossref",
      "first-page": "10482",
      "DOI": "10.1063/1.478977",
      "volume": "110",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021016532343900_r10",
      "doi-asserted-by": "crossref",
      "first-page": "5947",
      "DOI": "10.1063/1.479890",
      "volume": "111",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021016532343900_r11",
      "doi-asserted-by": "crossref",
      "first-page": "9258",
      "DOI": "10.1063/1.473004",
      "volume": "105",
      "year": "1996",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021016532343900_r12",
      "doi-asserted-by": "crossref",
      "first-page": "1198",
      "DOI": "10.1063/1.454720",
      "volume": "88",
      "year": "1988",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021016532343900_r13",
      "doi-asserted-by": "crossref",
      "first-page": "5331",
      "DOI": "10.1103/PhysRevE.54.5331",
      "volume": "54",
      "year": "1996",
      "journal-title": "Phys. Rev. E"
    },
    {
      "key": "2024021016532343900_r14",
      "doi-asserted-by": "crossref",
      "first-page": "1222",
      "DOI": "10.1103/PhysRevA.31.1222",
      "volume": "31",
      "year": "1985",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024021016532343900_r15",
      "first-page": "5002",
      "volume": "61",
      "year": "2000",
      "journal-title": "Phys. Rev. E"
    },
    {
      "key": "2024021016532343900_r16",
      "doi-asserted-by": "crossref",
      "first-page": "4711",
      "DOI": "10.1088/0305-4470/26/18/032",
      "volume": "26",
      "year": "1993",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024021016532343900_r17",
      "doi-asserted-by": "crossref",
      "first-page": "2391",
      "DOI": "10.1103/PhysRevB.37.2391",
      "volume": "37",
      "year": "1988",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024021016532343900_r18",
      "doi-asserted-by": "crossref",
      "first-page": "577",
      "DOI": "10.1142/S0217984999000737",
      "volume": "13",
      "year": "1999",
      "journal-title": "Mod. Phys. Lett. B"
    },
    {
      "key": "2024021016532343900_r19",
      "doi-asserted-by": "crossref",
      "first-page": "5338",
      "DOI": "10.1103/PhysRevA.41.5338",
      "volume": "41",
      "year": "1990",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024021016532343900_r20",
      "first-page": "L3991",
      "volume": "33",
      "year": "2000",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024021016532343900_r21",
      "doi-asserted-by": "crossref",
      "first-page": "L585",
      "DOI": "10.1088/0305-4470/30/16/005",
      "volume": "30",
      "year": "1997",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024021016532343900_r22",
      "doi-asserted-by": "crossref",
      "first-page": "L291",
      "DOI": "10.1088/0305-4470/14/8/007",
      "volume": "14",
      "year": "1981",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024021016532343900_r23",
      "doi-asserted-by": "crossref",
      "first-page": "L131",
      "DOI": "10.1088/0305-4470/22/4/004",
      "volume": "22",
      "year": "1989",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024021016532343900_r24",
      "doi-asserted-by": "crossref",
      "first-page": "770",
      "DOI": "10.1103/PhysRevB.9.770",
      "volume": "9",
      "year": "1974",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024021016532343900_r25",
      "doi-asserted-by": "crossref",
      "first-page": "3195",
      "DOI": "10.1103/PhysRevLett.57.3195",
      "volume": "57",
      "year": "1986",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021016532343900_r26",
      "doi-asserted-by": "crossref",
      "first-page": "258",
      "DOI": "10.1093/biomet/55.1.258",
      "volume": "55",
      "year": "1968",
      "journal-title": "Biometrika"
    },
    {
      "key": "2024021016532343900_r27",
      "doi-asserted-by": "crossref",
      "first-page": "209",
      "DOI": "10.1093/biomet/59.1.209",
      "volume": "59",
      "year": "1972",
      "journal-title": "Biometrika"
    },
    {
      "key": "2024021016532343900_r28",
      "doi-asserted-by": "crossref",
      "first-page": "207",
      "DOI": "10.1093/biomet/59.1.207",
      "volume": "59",
      "year": "1972",
      "journal-title": "Biometrika"
    },
    {
      "key": "2024021016532343900_r29",
      "doi-asserted-by": "crossref",
      "first-page": "1421",
      "DOI": "10.1103/PhysRevB.10.1421",
      "volume": "10",
      "year": "1974",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024021016532343900_r30",
      "doi-asserted-by": "crossref",
      "first-page": "393",
      "DOI": "10.1051/jphys:01974003505039300",
      "volume": "35",
      "year": "1974",
      "journal-title": "J. Phys. (Paris)"
    },
    {
      "key": "2024021016532343900_r31",
      "doi-asserted-by": "crossref",
      "first-page": "813",
      "DOI": "10.1051/jphys:01976003707-8081300",
      "volume": "37",
      "year": "1976",
      "journal-title": "J. Phys. (Paris)"
    },
    {
      "key": "2024021016532343900_r32",
      "doi-asserted-by": "crossref",
      "first-page": "1547",
      "DOI": "10.1088/0305-4470/10/9/013",
      "volume": "10",
      "year": "1977",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024021016532343900_r33",
      "doi-asserted-by": "crossref",
      "first-page": "4956",
      "DOI": "10.1063/1.456595",
      "volume": "90",
      "year": "1989",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021016532343900_r34",
      "doi-asserted-by": "crossref",
      "first-page": "6153",
      "DOI": "10.1063/1.460401",
      "volume": "94",
      "year": "1991",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021016532343900_r35",
      "first-page": "230",
      "volume": "57",
      "year": "1998",
      "journal-title": "Phys. Rev. E"
    },
    {
      "key": "2024021016532343900_r36",
      "doi-asserted-by": "crossref",
      "first-page": "8147",
      "DOI": "10.1088/0305-4470/31/40/009",
      "volume": "31",
      "year": "1998",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024021016532343900_r37",
      "doi-asserted-by": "crossref",
      "first-page": "961",
      "DOI": "10.1023/A:1018648130343",
      "volume": "98",
      "year": "2000",
      "journal-title": "J. Stat. Phys."
    },
    {
      "key": "2024021016532343900_r38"
    },
    {
      "key": "2024021016532343900_r39",
      "doi-asserted-by": "crossref",
      "first-page": "3009",
      "DOI": "10.1088/0305-4470/17/15/018",
      "volume": "17",
      "year": "1984",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024021016532343900_r40",
      "doi-asserted-by": "crossref",
      "first-page": "5351",
      "DOI": "10.1088/0305-4470/30/15/021",
      "volume": "30",
      "year": "1997",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024021016532343900_r41"
    },
    {
      "key": "2024021016532343900_r42"
    },
    {
      "key": "2024021016532343900_r43",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1088/0305-4470/32/1/004",
      "volume": "32",
      "year": "1999",
      "journal-title": "J. Phys. A"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/114/8/3659/19017114/3659_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/114/8/3659/19017114/3659_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        10
      ]
    ],
    "date-time": "2024-02-10T17:43:01Z",
    "timestamp": 1707586981000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/114/8/3659/184870/Precise-determination-of-the-critical-percolation"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2001,
        2,
        22
      ]
    ]
  },
  "references-count": 43,
  "journal-issue": {
    "issue": "8",
    "published-print": {
      "date-parts": [
        [
          2001,
          2,
          22
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1338506",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2001,
        2,
        22
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2001,
        2,
        22
      ]
    ]
  }
}