Fermionic field theory for trees and forests

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

    Research output: Contribution to journalArticle

    Abstract

    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)
    JournalPhysical Review Letters
    Volume93
    Issue number8
    DOIs
    StatePublished - Aug 20 2004

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    theorems
    fermions
    matrices

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    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). https://doi.org/10.1103/PhysRevLett.93.080601

    Fermionic field theory for trees and forests. / Caracciolo, Sergio; Jacobsen, Jesper Lykke; Saleur, Hubert; Sokal, Alan D.; Sportiello, Andrea.

    In: Physical Review Letters, Vol. 93, No. 8, 20.08.2004.

    Research output: Contribution to journalArticle

    Caracciolo, S, Jacobsen, JL, Saleur, H, Sokal, AD & Sportiello, A 2004, 'Fermionic field theory for trees and forests', Physical Review Letters, vol. 93, no. 8. https://doi.org/10.1103/PhysRevLett.93.080601
    Caracciolo S, Jacobsen JL, Saleur H, Sokal AD, Sportiello A. Fermionic field theory for trees and forests. Physical Review Letters. 2004 Aug 20;93(8). https://doi.org/10.1103/PhysRevLett.93.080601
    Caracciolo, Sergio ; Jacobsen, Jesper Lykke ; Saleur, Hubert ; Sokal, Alan D. ; Sportiello, Andrea. / Fermionic field theory for trees and forests. In: Physical Review Letters. 2004 ; Vol. 93, No. 8.
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