We compute in small temperature expansion the two-loop renormalization constants and the three-loop coefficient of the beta-function, that is the first non-universal term, for the sigma-model with O(N) invariance on the triangular lattice at N=-1. The partition function of the corresponding Grassmann theory is, for negative temperature, the generating function of unrooted forests on such a lattice, where the temperature acts as a chemical potential for the number of trees in the forest. To evaluate Feynman diagrams we extend the coordinate space method to the triangular lattice.
Renormalization flow for unrooted forests on a triangular lattice / S. Caracciolo, C. De Grandi, A. Sportiello. - In: NUCLEAR PHYSICS. B. - ISSN 0550-3213. - 787:3(2007), pp. 260-282. [10.1016/j.nuclphysb.2007.06.012]
Renormalization flow for unrooted forests on a triangular lattice
S. CaraccioloPrimo
;A. SportielloUltimo
2007
Abstract
We compute in small temperature expansion the two-loop renormalization constants and the three-loop coefficient of the beta-function, that is the first non-universal term, for the sigma-model with O(N) invariance on the triangular lattice at N=-1. The partition function of the corresponding Grassmann theory is, for negative temperature, the generating function of unrooted forests on such a lattice, where the temperature acts as a chemical potential for the number of trees in the forest. To evaluate Feynman diagrams we extend the coordinate space method to the triangular lattice.Pubblicazioni consigliate
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