Nonlinear excitations in the critical region

The free energy transformation due to fluctuations is investigated in an exactly solvable model. This model accounts for the fluctuation interaction in a reduced manner and leads to a realistic estimation for the free energy. In particular it gives a nice critical exponent=5. It is shown that in spite of the monotonic character of the effective free energy in the critical region the properties of the system should be described on the basis of the⁶ model. Localized nonlinear excitations are found to be possible with a profile rather like that known as a bump near the point of the first-order phase transition.