Data di Pubblicazione:
2009
Citazione:
Spanning forests on random planar lattices / S. Caracciolo, A. Sportiello. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 135:5-6(2009), pp. 1063-1104.
Abstract:
The generating function for spanning forests on a lattice is related to the q-state Potts model in a certain q
to 0 limit, and extends the analogous notion for spanning trees, or dense self-avoiding branched polymers. Recent works have found a combinatorial perturbative equivalence also with the (quadratic action) O(n) model
in the limit n to -1, the expansion parameter t counting the number of components of the forest.
We give a random-matrix formulation of this model on the ensemble of degree-k random planar lattices. For k=3, a correspondence is found with the Kostov solution of the loop-gas problem, which arise as
a reformulation of the (logarithmic action) O(n) model, at n=-2.
Then, we show how to perform an expansion around the t=0 theory. In
the thermodynamic limit, at any order in $t$ we have a finite sum of
finite-dimensional Cauchy integrals. The leading contribution comes from a
peculiar class of terms, for which a resummation can be performed
exactly.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
O(n)-invariant σ-model; O(n)-vector model; Potts model; Random matrices; Self-avoiding polymers; Spanning forests; Spanning trees
Elenco autori:
S. Caracciolo, A. Sportiello
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