97-27E

A simple hierarchical scalar spin model is studied analytically and numerically in the vicinity of its critical point. The dependence of the finite size (i.e. calculated for large but finite number of spins) susceptibility and the location of zeros of the model partition function, on the number of spins at the critical point is described analytically. It is shown, also analytically, that the finite size correlation length in such a model diverges at the critical point slowly than it is supposed in the finite size scaling theory. Certain numerical information about the critical point and ordered phase is given. In particular, the critical temperature of the model and the critical index describing the order parameter are calculated for various values of the interaction parameter.