Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice

John Cardy, Jesper Lykke Jacobsen, Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review


    At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2; and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as β ≡ J / kT → ∞ according to ξ ∼ Ae2β(1+bβe-β+⋯), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.

    Original languageEnglish (US)
    Pages (from-to)25-47
    Number of pages23
    JournalJournal of Statistical Physics
    Issue number1-2
    StatePublished - Oct 2001


    • Antiferromagnetic Potts model
    • Corrections to scaling
    • Height representation
    • Renormalization group
    • Six-vertex model

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics


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