If A$_{k}$ is symmetric for real Gaussian integrals as in (51) and (52) we have: 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: Finally, the correlation functions for the magnetic and electric subsystems take the form: Using: we obtain the correlation function in the Ornstein-Zernike form: ∫ d⃗ η$_{k}$e 1 $_{2}$⃗ η T $_{k}$A$_{k}$ ⃗ $^{η$_{k}$}$η$_{i}$ η$_{j}$ = (2 π ) N 2 ( det A ) − 1 2 A − 1 ij , (53) 〈 δp$_{-k}$δp$_{k}$ 〉 = A − 1 11 + A − 1 22 = k$_{B}$T 2 C$_{m}$ ( A$_{m}$ + 1 $_{2}$a$_{3}$ k $^{2}$) , (54) 〈 δm$_{-k}$δm$_{k}$ 〉 = A − 1 33 + A − 1 44 = k$_{B}$T 2 C$_{m}$ ( B$_{m}$ + 1 $_{2}$k$^{2}$) , (55) 〈 δp$_{1k}$m$_{1k}$ + δp$_{2k}$m$_{2k}$ 〉 = A − 1 31 + A − 1 42 = k$_{B}$T C$_{m}$γ$_{me}$ . (56) g$_{p}$ ( ⃗ r$_{1}$, ⃗ r$_{2}$ ) = 〈 δp ( ⃗ r$_{1}$ ) δp ( ⃗ r$_{2}$ ) 〉 (57) = ∫ d $^{3}$k (2 π ) 3 〈 δp$_{-k}$δp$_{k}$ 〉 e i k · ( ⃗ r$_{2}$ − ⃗ r$_{1}$ ) = ∫ d $^{3}$k (2 π ) 3 · k$_{B}$T 2 C$_{m}$ ( A$_{m}$ + 1 $_{2}$a$_{3}$ k $^{2}$) e i k · ( ⃗ r$_{2}$ − ⃗ r$_{1}$ $^{)}$, g$_{m}$ ( ⃗ r$_{1}$, ⃗ r$_{2}$ ) = 〈 δm ( ⃗ r$_{1}$ ) δm ( ⃗ r$_{2}$ ) 〉 (58) = ∫ d $^{3}$k (2 π ) 3 〈 δm$_{-k}$δm$_{k}$ 〉 e i k · ( ⃗ r$_{2}$ − ⃗ r$_{1}$ ) = ∫ d $^{3}$k (2 π ) 3 · k$_{B}$T 2 C$_{m}$ ( B$_{m}$ + 1 $_{2}$k$^{2}$) e i k · ( ⃗ r$_{2}$ − ⃗ r$_{1}$ $^{)}$. ∫ d $^{3}$k (2 π ) 3 1 k 2 + a $_{2}$e i ⃗ k · ⃗ r = e − ar 4 πr , g$_{p}$ ( ⃗ r$_{1}$, ⃗ r$_{2}$ ) = k$_{B}$T C$_{m}$a$_{3}$ · e − √ 2 A m a 3 | ⃗ r$_{2}$ − ⃗ r$_{1}$ | 4 π | ⃗ r$_{2}$ − ⃗ r$_{1}$ | ≡ k$_{B}$T C$_{m}$a$_{3}$ · e − | ⃗ r 2 − ⃗ r 1 | ξ m 4 π | ⃗ r$_{2}$ − ⃗ r$_{1}$ | , (59) 20