Genus one contribution to free energy in Hermitian two-matrix model Original Research Article

We compute the genus one correction to free energy of Hermitian two-matrix model in large N limit in terms of theta-functions associated to the spectral curve. We discuss the relationship of this expression to the isomonodromic tau-function, the Bergmann tau-function on Hurwitz spaces, the G-function of Frobenius manifolds and the determinant of Laplacian in a singular metric over the spectral curve.