Fermionic field theory for trees and forests

Sergio Caracciolo, Jesper Lykke Jacobsen, Hubert Saleur, Alan D. Sokal, Andrea Sportiello

    Research output: Contribution to journalArticle


    The Kirchhoff's matrix-tree theorem which contained a large class of combinatorial ojbects represented by non-Gaussian Grassmann integrals was discussed. It was shown that unrooted spanning forests, which arise as a q→0 limit of the Potts model, can be represented by a Grassmann theory involving a Gaussian term and a particular bilocal four-fermion term. This fermionic model due to its simplicity, was found to be the most viable candidate for a rigorous nonperturbative proof of asymptotic freedom. The results show that in two dimensions, this fermionic model is perturbatively asymptotically free.

    Original languageEnglish (US)
    Pages (from-to)080601-1-080601-4
    JournalPhysical Review Letters
    Issue number8
    StatePublished - Aug 20 2004

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

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  • Cite this

    Caracciolo, S., Jacobsen, J. L., Saleur, H., Sokal, A. D., & Sportiello, A. (2004). Fermionic field theory for trees and forests. Physical Review Letters, 93(8), 080601-1-080601-4. https://doi.org/10.1103/PhysRevLett.93.080601