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Free energy topological expansion for the 2-matrix model

Leonid Chekhov·Bertrand Eynard·Nicolas Orantin
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Abstract

We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/ N expansion of the nonmixed correlation functions and give a new formulation of the spectral curve. We extend these rules obtaining a closed formula for correlation functions in all orders of topological expansion. We then integrate it to obtain the free energy in terms of residues on the associated Riemann surface.

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Leonid Chekhov, Bertrand Eynard, Nicolas Orantin. 2006-03-03. Free energy topological expansion for the 2-matrix model. https://doi.org/10.1088/1126-6708%2F2006%2F12%2F053

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