Genus one contribution to free energy in hermitian two-matrix model

We compute an the genus 1 correction to free energy of Hermitian two-matrix model in terms of theta-functions associated to spectral curve arising in large N limit. We discuss the relationship of this expression to isomonodromic tau-function, Bergmann tau-function on Hurwitz spaces, G-function of Frobenius manifolds and determinant of Laplacian in a singular metric over spectral curve.