we obtain the following expression for the free energy: In order to evaluate the value of the fluctuations we have to take an average of all the possible configurations. One can define the statistical sum for a system with two order parameters as an integral over all existing profiles for each of the order parameters: Because δm$_{k}$ and δp$_{k}$ are complex numbers we can represent them in the following way: As may be seen δm$_{k}$ and δm$_{-k}$ are not independent. In order to avoid double counting for δm$_{k}$ and δm$_{-k}$ we have to take only wave vectors k with k$_{z}$ > 0 (the same applies for δp ). Thus, the partition function representing the Gaussian fluctuations takes the form: where the corresponding free energy functional is For further calculations we use matrix notation: 24 δF = C$_{m}$ ∑ k ( A$_{m}$ + 1 2 a$_{3}$ k $^{2}$) δp$_{k}$δp$_{-k}$ (A5) + C$_{m}$ ∑ k ( B$_{m}$ + 1 2 k $^{2}$) δm$_{k}$δm$_{-k}$ + 1 2 C$_{m}$γ$_{me}$ ∑ k [ δm$_{k}$δp$_{-k}$ + δm$_{-k}$δp$_{k}$ ] . Z = ∏ k ∫ D ( δm$_{k}$ ) D ( δp$_{k}$ ) e − δF ( δm,δp ) k B T . (A6) δm$_{k}$ = δm$_{1k}$ + i · δm$_{2k}$, (A7) δp$_{k}$ = δp$_{1k}$ + i · δp$_{2k}$. (A8) Z = ∏ k ,k$_{z}$> 0 ∫ ∞ −∞ D ( δm$_{1k}$ )$^{∫}$ ∞ −∞ D ( δm$_{2k}$ )$^{∫}$ ∞ −∞ D ( δp$_{1k}$ )$^{∫}$ ∞ −∞ D ( δp$_{2k}$ ) e − δF ( δm,δp ) k B T , (A9) δF = 2 C$_{m}$ ∑ k ,k$_{z}$> 0 ( A$_{m}$ + 1 2 a$_{3}$ k $^{2}$)( δp 2 1k + δp 2 $_{2k}$) (A10) + 2 C$_{m}$ ∑ k ,k$_{z}$> 0 ( B$_{m}$ + 1 2 k $^{2}$)( δm 2 1k + δm 2 $_{2k}$) + 2 C$_{m}$γ$_{me}$ ∑ k ,k$_{z}$> 0 ( δm$_{1k}$δp$_{1k}$ + δm$_{2k}$δp$_{2k}$ ) .