Free energy topological expansion for the 2-matrix model.

Leonid Chekhov (1, 2, 3) , Bertrand Eynard (4) , Nicolas Orantin (4)

1 ISCP - Interdisciplinary Scientific Center Poncelet
2 ITEP - Institute of Theoretical and Experimental Physics [Moscow]
3 SMI | RAS - Steklov Mathematical Institute [Moscow]
4 SPhT - Service de Physique Théorique

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.

Mots clés: Random matrices; algebraic geometry; topological expansion; spectral curve

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]

Leonid Chekhov, Bertrand Eynard, Nicolas Orantin. Free energy topological expansion for the 2-matrix model.. 2006. ⟨hal-00019891v2⟩