Enumeration of maps with self-avoiding loops and the \mathcal {O}(\mathfrak {n}) model on random lattices of all topologies

DOI10.1088/1742-5468/2011/01/P01010zbMath1456.82430arXiv0910.5896MaRDI QIDQ3301204

Gaëtan Borot, Bertrand Eynard

Publication date: 11 August 2020

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.5896

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Planar graphs; geometric and topological aspects of graph theory (05C10) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41)

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Cites Work

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• Three-spin strings on \(\mathrm{AdS}_{5}\times S^{5}\) from \(\mathcal N=4\) SYM
• Conformal boundary loop models
• Genus one contribution to free energy in Hermitian two-matrix model
• Invariants of algebraic curves and topological expansion
• Planar diagrams
• Exact solution of the \(O(n)\) model on a random lattice
• More on the exact solution of the \(O(n)\) model on a random lattice and an investigation of the case \(|n|>2\)
• Matrix model calculations beyond the spherical limit.
• Phase structure of the \(O(n)\) model on a random lattice for \(n> 2\)
• A Census of Planar Triangulations
• LIOUVILLE FIELD THEORY: A DECADE AFTER THE REVOLUTION
• Boundary loop models and 2D quantum gravity
• A Census of Planar Maps
• The Potts-\(q\) random matrix model: Loop equations, critical exponents, and rational case.