99-09U

The general expression for coefficients of the total functional of the cluster de-Jennes model free energy is found. They are expressed by an arbitrary order cumulant averages of the generalized transition operators products. It is shown that the transverse field increase leads to the sign change of all higher Gaussian order coeficients. An equation for maximum transverse field magnitude, short-range interaction and temperature providing the finite expression for the free energy functional is found.