Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies

Details Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies

2009-10-30

arxiv.org/abs/0910.5896v2

J.Stat.Mech.2011:P01010,2011

Physics

Mathematical Physics

pdflatex, 89 pages, 12 labelled figures (15 figures at all), minor corrections

Scientific paper

We compute the generating functions of a O(n) model (loop gas model) on a random lattice of any topology. On the disc and the cylinder, they were already known, and here we compute all the other topologies. We find that the generating functions (and the correlation functions of the lattice) obey the topological recursion, as usual in matrix models, i.e they are given by the symplectic invariants of their spectral curve.

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