content_image/348356.jpg content_image/348357.jpg content_image/348358.jpg content_image/348359.jpg content_image/348360.jpg content_image/348361.jpg content_image/348362.jpg content_image/348363.jpg
If A$_{k}$ is symmetric for real Gaussian integrals as in (51) and (52) we have: 

<img src='content_image/348356.jpg'>

where A$_{ij}$ - is an element of the A$_{k}$ matrix in the i th - row and j th-column, η$_{i}$ for i = 1 , 2 , 3 , 4 is an element of the vector ⃗ η$_{k}$ . 

We obtain following expressions: 

and for the cross-correlations we have: 

<img src='content_image/348357.jpg'>

<img src='content_image/348358.jpg'>

<img src='content_image/348359.jpg'>

Finally, the correlation functions for the magnetic and electric subsystems take the form: 

<img src='content_image/348360.jpg'>

<img src='content_image/348361.jpg'>

Using: 

we obtain the correlation function in the Ornstein-Zernike form: 

<img src='content_image/348362.jpg'>

<img src='content_image/348363.jpg'>

