Generalized hierarchical model of a scalar ferromagnet in the method of collective variables

By means of the method of collective variables and certain approximations a hierarchical representation is obtained for the partition function of the ferromagnetic Ising model with both short- and long-range interactions. It is shown that in the latter case the representation is, apart from a factor, identical to the exact representation of the partition function of the Dys0n model obtained by the same method. The approximations that lead from the Ising model to the Dyson model are analyzed.