content_image/347725.jpg content_image/347726.jpg content_image/347727.jpg content_image/347728.jpg content_image/347729.jpg content_image/347730.jpg
we obtain the following expression for the free energy: 

<img src='content_image/347725.jpg'>

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: 

<img src='content_image/347726.jpg'>

Because δm$_{k}$ and δp$_{k}$ are complex numbers we can represent them in the following way: 

<img src='content_image/347727.jpg'>

<img src='content_image/347728.jpg'>

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: 

<img src='content_image/347729.jpg'>

where the corresponding free energy functional is 

For further calculations we use matrix notation: 

<img src='content_image/347730.jpg'>

