Renormalization flow for unrooted forests on a triangular lattice

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.

26 pages, 4 figures

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Cited by in corpus (8)

• Grassmann Integral Representation for Spanning Hyperforests
• Explicit characterization of the identity configuration in an Abelian Sandpile Model
• Exact integration of height probabilities in the Abelian Sandpile Model
• Phase transition in the spanning-hyperforest model on complete hypergraphs
• Spanning Forests on Random Planar Lattices
• Hyperforests on the Complete Hypergraph by Grassmann Integral Representation
• Critical Behaviour of Spanning Forests on Random Planar Graphs
• Conformally Covariant Operators and Conformal Invariants on Weighted Graphs