  We use an m-vicinity method to examine Ising models on hypercube lattices of
high dimensions d>=3. This method is applicable for both short-range and
long-range interactions. We introduce a small parameter, which determines
whether the method can be used when calculating the free energy. When we
account for interaction with the nearest neighbors only, the value of this
parameter depends on the dimension of the lattice d. We obtain an expression
for the critical temperature in terms of the interaction constants that is in a
good agreement with results of computer simulations. For d=5, 6, 7, our
theoretical estimates match the experiments both qualitatively and
quantitatively. For d=3, 4, our method is sufficiently accurate for calculation
of the critical temperatures, however, it predicts a finite jump of the heat
capacity at the critical point. In the case of the three-dimensional lattice
(d=3), this contradicts to the commonly accepted ideas of the type of the
singularity at the critical point. For the four-dimensional lattice (d = 4) the
character of the singularity is under current discussion. For the dimensions
d=1, 2 the m-vicinity method is not applicable.
