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.
ASJC Scopus subject areas
- Physics and Astronomy(all)