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

Abstract

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.

39 pages, 18 figures, minor modifications

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Cited by in corpus (12)

• The three-point function of planar quadrangulations
• Distance statistics in quadrangulations with a boundary, or with a self-avoiding loop
• Statistics of geodesics in large quadrangulations
• Spanning forests in regular planar maps
• Liouville Quantum Gravity and KPZ
• Confluence of geodesic paths and separating loops in large planar quadrangulations
• On the number of planar Eulerian orientations
• Local convergence of large random triangulations coupled with an Ising model
• Planar maps and random partitions
• Ising model on random triangulations of the disk: phase transition
• Matrix integrals and enumeration of maps
• Combinatoire du polynôme de Tutte et des cartes planaires