Spanning Forests on Random Planar Lattices
نویسندگان
چکیده
منابع مشابه
Spanning Forests on Random Planar Lattices
The generating function for spanning forests on a lattice is related to the q-state Potts model in a certain q → 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 → −1, the expansion parameter t counting the number of c...
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As a follow-up of previous work of the authors, we analyse the statistical mechanics model of random spanning forests on random planar graphs. Special emphasis is given to the analysis of the critical behaviour. Exploiting an exact relation with a model of O(−2)-loops and dimers, previously solved by Kostov and Staudacher, we identify critical and multicritical loci, and find them consistent wi...
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We address the enumeration of p-valent planar maps equipped with a spanning forest, with a weight z per face and a weight u per connected component of the forest. Equivalently, we count p-valent maps equipped with a spanning tree, with a weight z per face and a weight μ := u + 1 per internally active edge, in the sense of Tutte; or the (dual) p-angulations equipped with a recurrent sandpile con...
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2009
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-009-9733-1