ABSTRACT
Let us now turn to a very important question of the applicability limits of Landau's phase transition theory both in the general context and in its application to superconductors [86].
Landau's phase transition theory [50, 34) is well known to be the mean field theory (or, as it is sometimes referred to, molecular or self-consistent field theory). This means that the free energy (or a corresponding thermodynamic potential) of the type
(7.37)
does not allow for the contribution from the fluctuations of ry. As we have seen in the example of a superconductor, when 7J = \]! (see
equations (7.12), (7.13)), below the second-order transition point (we set 'Y = 0), the equilibrium value is
2 a a~(Tc - T) rto = -{j = f3c . (7.38)
Taking the Landau theory as the first approximation and using it as a basis, one can find the fluctuations of various quantities, in particular, the parameter 7J itself. Naturally, the Landau theory holds true and the fluctuations calculated on its basis hold true only as long as they are small compared to the mean values obtained within the Landau theory. In application to ry, this means that the condition
(7.39)
must hold, where obviously (~ry)2 is the statistical mean of the fluctuation of the quantity 7J (the fluctuation (~ry) is zero because we calculate the deviations from the value 7Jo corresponding to the minimum free energy).
