1/N2 correction to free energy in Hermitian two-matrix model

Using the loop equations we find an explicit expression for genus I correction in hermitian two-matrix model in terms of holomorphic objects associated to spectral curve arising in large N limit. Our result generalises known expression for F-1 in hermitian one-matrix model. We discuss the relationship between F-1, Bergman tau-function on Hurwitz spaces, G-function of Frobenius manifolds and determinant of Laplacian over spectral curve.