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 journalArticlepeer-review

    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

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

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