  The problem of finding a microscopic theory of phase transitions across a
critical point is a central unsolved problem in theoretical physics. We find a
general solution to that problem and present it here for the cases of
Bose-Einstein condensation in an interacting gas and ferromagnetism in a
lattice of spins, interacting via a Heisenberg or Ising Hamiltonian. For
Bose-Einstein condensation, we present the exact, valid for the entire critical
region, equations for the Green functions and order parameter, that is a
critical-region extension of the Beliaev-Popov and Gross-Pitaevskii equations.
For the magnetic phase transition, we find an exact theory in terms of
constrained bosons in a lattice and obtain similar equations for the Green
functions and order parameter. In particular, we outline an exact solution for
the three-dimensional Ising model.
