  The new approach to the microscopic description of the phase transitions
starting from the only first principles was developed on an example of the
transition normal metal-superconductor. This means mathematically, that the
free energy is calculated in the range of temperatures, which includes a point
of pase transition, without introducing any artificial parameters similar to an
order parameter, but only starting from microscopic parameters of Hamiltonian.
Moreover the theorems about connection of a vacuum amplitude with
thermodynamics potentials are realized. The functional of a superconductor's
free energy in a magnetic field was obtained with help the developed method.
The obtained functional is generalization of Ginzburg-Landau functional for the
case of arbitrary value of a gap, arbitrary spatial inhomogeneities and
nonlocal magnetic response. The explicit expressions for the extremals of this
functional were obtained in the low-temperature limit and the high-temperature
limit at the condition of slowness of gap's changes.
