Asymptotic scaling in the two-dimensional O(3) σ model at correlation length 105

Sergio Caracciolo, Robert G. Edwards, Andrea Pelissetto, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We carry out a high-precision Monte Carlo simulation of the two-dimensional O(3)-invariant σ model at correlation lengths ξ up to ∼105. Our work employs a powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is 25% at ξ∼102, decreases to 4% at ξ∼105.

    Original languageEnglish (US)
    Pages (from-to)1891-1894
    Number of pages4
    JournalPhysical Review Letters
    Volume75
    Issue number10
    DOIs
    StatePublished - 1995

    Fingerprint

    scaling
    systematic errors
    extrapolation
    deviation
    predictions
    simulation

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Asymptotic scaling in the two-dimensional O(3) σ model at correlation length 105. / Caracciolo, Sergio; Edwards, Robert G.; Pelissetto, Andrea; Sokal, Alan D.

    In: Physical Review Letters, Vol. 75, No. 10, 1995, p. 1891-1894.

    Research output: Contribution to journalArticle

    Caracciolo, S, Edwards, RG, Pelissetto, A & Sokal, AD 1995, 'Asymptotic scaling in the two-dimensional O(3) σ model at correlation length 105', Physical Review Letters, vol. 75, no. 10, pp. 1891-1894. https://doi.org/10.1103/PhysRevLett.75.1891
    Caracciolo, Sergio ; Edwards, Robert G. ; Pelissetto, Andrea ; Sokal, Alan D. / Asymptotic scaling in the two-dimensional O(3) σ model at correlation length 105. In: Physical Review Letters. 1995 ; Vol. 75, No. 10. pp. 1891-1894.
    @article{fc3a5e84293c4622b38919b229e40b08,
    title = "Asymptotic scaling in the two-dimensional O(3) σ model at correlation length 105",
    abstract = "We carry out a high-precision Monte Carlo simulation of the two-dimensional O(3)-invariant σ model at correlation lengths ξ up to ∼105. Our work employs a powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is 25{\%} at ξ∼102, decreases to 4{\%} at ξ∼105.",
    author = "Sergio Caracciolo and Edwards, {Robert G.} and Andrea Pelissetto and Sokal, {Alan D.}",
    year = "1995",
    doi = "10.1103/PhysRevLett.75.1891",
    language = "English (US)",
    volume = "75",
    pages = "1891--1894",
    journal = "Physical Review Letters",
    issn = "0031-9007",
    publisher = "American Physical Society",
    number = "10",

    }

    TY - JOUR

    T1 - Asymptotic scaling in the two-dimensional O(3) σ model at correlation length 105

    AU - Caracciolo, Sergio

    AU - Edwards, Robert G.

    AU - Pelissetto, Andrea

    AU - Sokal, Alan D.

    PY - 1995

    Y1 - 1995

    N2 - We carry out a high-precision Monte Carlo simulation of the two-dimensional O(3)-invariant σ model at correlation lengths ξ up to ∼105. Our work employs a powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is 25% at ξ∼102, decreases to 4% at ξ∼105.

    AB - We carry out a high-precision Monte Carlo simulation of the two-dimensional O(3)-invariant σ model at correlation lengths ξ up to ∼105. Our work employs a powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is 25% at ξ∼102, decreases to 4% at ξ∼105.

    UR - http://www.scopus.com/inward/record.url?scp=4243442479&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=4243442479&partnerID=8YFLogxK

    U2 - 10.1103/PhysRevLett.75.1891

    DO - 10.1103/PhysRevLett.75.1891

    M3 - Article

    VL - 75

    SP - 1891

    EP - 1894

    JO - Physical Review Letters

    JF - Physical Review Letters

    SN - 0031-9007

    IS - 10

    ER -