Some geometric critical exponents for percolation and the random-cluster model

Youjin Deng, Wei Zhang, Timothy M. Garoni, Alan D. Sokal, Andrea Sportiello

    Research output: Contribution to journalArticle

    Abstract

    We introduce several infinite families of critical exponents for the random-cluster model and present scaling arguments relating them to the k -arm exponents. We then present Monte Carlo simulations confirming these predictions. These exponents provide a convenient way to determine k -arm exponents from Monte Carlo simulations. An understanding of these exponents also leads to a radically improved implementation of the Sweeny Monte Carlo algorithm. In addition, our Monte Carlo data allow us to conjecture an exact expression for the shortest-path fractal dimension dmin in two dimensions: dmin =? (g+2) (g+18) / (32g), where g is the Coulomb-gas coupling, related to the cluster fugacity q via q=2+2cos (gπ/2) with 2≤g≤4.

    Original languageEnglish (US)
    Article number020102
    JournalPhysical Review E
    Volume81
    Issue number2
    DOIs
    StatePublished - Feb 10 2010

    Fingerprint

    Random-cluster Model
    Critical Exponents
    Exponent
    exponents
    Monte Carlo Simulation
    Coulomb Gas
    Monte Carlo Algorithm
    Fractal Dimension
    Shortest path
    Two Dimensions
    Scaling
    fractals
    simulation
    Prediction
    scaling
    predictions
    gases

    ASJC Scopus subject areas

    • Condensed Matter Physics
    • Statistical and Nonlinear Physics
    • Statistics and Probability

    Cite this

    Deng, Y., Zhang, W., Garoni, T. M., Sokal, A. D., & Sportiello, A. (2010). Some geometric critical exponents for percolation and the random-cluster model. Physical Review E, 81(2), [020102]. https://doi.org/10.1103/PhysRevE.81.020102

    Some geometric critical exponents for percolation and the random-cluster model. / Deng, Youjin; Zhang, Wei; Garoni, Timothy M.; Sokal, Alan D.; Sportiello, Andrea.

    In: Physical Review E, Vol. 81, No. 2, 020102, 10.02.2010.

    Research output: Contribution to journalArticle

    Deng, Y, Zhang, W, Garoni, TM, Sokal, AD & Sportiello, A 2010, 'Some geometric critical exponents for percolation and the random-cluster model', Physical Review E, vol. 81, no. 2, 020102. https://doi.org/10.1103/PhysRevE.81.020102
    Deng, Youjin ; Zhang, Wei ; Garoni, Timothy M. ; Sokal, Alan D. ; Sportiello, Andrea. / Some geometric critical exponents for percolation and the random-cluster model. In: Physical Review E. 2010 ; Vol. 81, No. 2.
    @article{53c57bfa46db468db931a945985ae2be,
    title = "Some geometric critical exponents for percolation and the random-cluster model",
    abstract = "We introduce several infinite families of critical exponents for the random-cluster model and present scaling arguments relating them to the k -arm exponents. We then present Monte Carlo simulations confirming these predictions. These exponents provide a convenient way to determine k -arm exponents from Monte Carlo simulations. An understanding of these exponents also leads to a radically improved implementation of the Sweeny Monte Carlo algorithm. In addition, our Monte Carlo data allow us to conjecture an exact expression for the shortest-path fractal dimension dmin in two dimensions: dmin =? (g+2) (g+18) / (32g), where g is the Coulomb-gas coupling, related to the cluster fugacity q via q=2+2cos (gπ/2) with 2≤g≤4.",
    author = "Youjin Deng and Wei Zhang and Garoni, {Timothy M.} and Sokal, {Alan D.} and Andrea Sportiello",
    year = "2010",
    month = "2",
    day = "10",
    doi = "10.1103/PhysRevE.81.020102",
    language = "English (US)",
    volume = "81",
    journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",
    issn = "1539-3755",
    publisher = "American Physical Society",
    number = "2",

    }

    TY - JOUR

    T1 - Some geometric critical exponents for percolation and the random-cluster model

    AU - Deng, Youjin

    AU - Zhang, Wei

    AU - Garoni, Timothy M.

    AU - Sokal, Alan D.

    AU - Sportiello, Andrea

    PY - 2010/2/10

    Y1 - 2010/2/10

    N2 - We introduce several infinite families of critical exponents for the random-cluster model and present scaling arguments relating them to the k -arm exponents. We then present Monte Carlo simulations confirming these predictions. These exponents provide a convenient way to determine k -arm exponents from Monte Carlo simulations. An understanding of these exponents also leads to a radically improved implementation of the Sweeny Monte Carlo algorithm. In addition, our Monte Carlo data allow us to conjecture an exact expression for the shortest-path fractal dimension dmin in two dimensions: dmin =? (g+2) (g+18) / (32g), where g is the Coulomb-gas coupling, related to the cluster fugacity q via q=2+2cos (gπ/2) with 2≤g≤4.

    AB - We introduce several infinite families of critical exponents for the random-cluster model and present scaling arguments relating them to the k -arm exponents. We then present Monte Carlo simulations confirming these predictions. These exponents provide a convenient way to determine k -arm exponents from Monte Carlo simulations. An understanding of these exponents also leads to a radically improved implementation of the Sweeny Monte Carlo algorithm. In addition, our Monte Carlo data allow us to conjecture an exact expression for the shortest-path fractal dimension dmin in two dimensions: dmin =? (g+2) (g+18) / (32g), where g is the Coulomb-gas coupling, related to the cluster fugacity q via q=2+2cos (gπ/2) with 2≤g≤4.

    UR - http://www.scopus.com/inward/record.url?scp=77249148424&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=77249148424&partnerID=8YFLogxK

    U2 - 10.1103/PhysRevE.81.020102

    DO - 10.1103/PhysRevE.81.020102

    M3 - Article

    VL - 81

    JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

    JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

    SN - 1539-3755

    IS - 2

    M1 - 020102

    ER -