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. Caracciolo
Primo
;
A. Sportiello
Ultimo
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.
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
2007
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/39104
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? 10
social impact