On the two- and three-dimensional Ising-Onsager problem in presence of magnetic field

In this paper a new approach to solving: the Ising-Onsager problem in external magnetic field is investigated. The expression for free energy per Ising spill in external field both for the two dimensional and three dimensional Ising model with interaction of the nearest neighbors: are derived. The representations of free energy being expressed by multidimensional integrals of Gauss type with the appropriate dimensionality are shown. The possibility of calculating the integrals and the critical indices on the base of the derived representations for free energy is investigated.