Blocked edges on Eulerian maps and mobiles: Application to spanning trees, hard particles and the Ising model

Details Blocked edges on Eulerian maps and mobiles: Application to spanning trees, hard particles and the Ising model Blocked edges on Eulerian maps and mobiles: Application to spanning trees, hard particles and the Ising model

2007-02-05

arxiv.org/abs/math/0702097v2

J. Phys. A: Math. Theor. 40 (2007) 7411-7440

Mathematics

Combinatorics

39 pages, 18 figures, minor modifications

Scientific paper

10.1088/1751-8113/40/27/002

We introduce Eulerian maps with blocked edges as a general way to implement statistical matter models on random maps by a modification of intrinsic distances. We show how to code these dressed maps by means of mobiles, i.e. decorated trees with labeled vertices, leading to a closed system of recursion relations for their generating functions. We discuss particular solvable cases in detail, as well as various applications of our method to several statistical systems such as spanning trees on quadrangulations, mutually excluding particles on Eulerian triangulations or the Ising model on quadrangulations.

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