After substituting (37) and (38) into (37) we expand the expression for the free energy density. For simplicity, we retain only the second order terms: The constant expression: gives the mean filed value of the free energy density. Linear terms in { δm, δp } vanish, because the mean field solution { M$_{0}$, P$_{0}$ } minimizes the free energy F . In effect, we obtain the contribution to the free energy coming from the fluctuations of the order parameters in the form: where: A$_{m}$ = a$_{1}$ 2 + 3 $_{2}$a$_{2}$ P 2 0 + 1 $_{2}$c$_{m}$ M 2 $_{0}$, B$_{m}$ = b$_{1}$ 2 + 3 $_{2}$M 2 0 + 1 $_{2}$c$_{m}$ P 2 $_{0}$, γ$_{me}$ = c$_{m}$ 2 P$_{0}$M$_{0}$ , and C$_{m}$ = Ω a 2 $_{0}$T 2 M b . With the help of the expression for the δF obtained above we calculate in the Appendix A the explicit form of the partition function Z , which takes into account spatial fluctuations of the two interacting order parameters. To calculate explicitly the contribution of the fluctuations to the specific heat we use the partition function (A17). The free energy part due to fluctuations can be written as: C. Specific heat 17 δF = C$_{m}$$^{∫ {}$A$_{m}$ ( δp ) 2 + B$_{m}$ ( δm ) 2 + 1 2 | ⃗ ∇ δm | 2 + a$_{3}$ 2 | ⃗ ∇ δp | 2 + γ$_{me}$δmδp$^{}}$ d $^{3}$r , (41) φ$_{0}$ = a$_{1}$ 2 P 2 0 + a$_{2}$ 4 P 4 0 + b$_{1}$ 2 M 2 0 + 1 4 M 4 0 + c$_{m}$ 2 P 2 $_{0}$M 2 $_{0}$, (40) ˜ φ ( ˜ M ( r ) , ˜ P ( r ) , T ) ≈ a$_{1}$ 2 P 2 0 + a$_{2}$ 4 P 4 0 + b$_{1}$ 2 M 2 0 (39) + 1 4 M 4 0 + c$_{m}$ 2 P 2 $_{0}$M 2 0 + δp $^{(}$a$_{1}$ P$_{0}$ + a$_{2}$P 3 0 + c$_{m}$P 2 $_{0}$M$_{0}$ ) + δm $^{(}$b$_{1}$ M$_{0}$ + M 3 0 + c$_{m}$P$_{0}$M 2 0 ) + ( δp ) 2 $^{(}$a$_{1}$ 2 + 3 2 a$_{2}$P 2 0 + 1 2 c$_{m}$M 2 0 ) + ( δm ) 2 $^{(}$b$_{1}$ 2 + 3 2 M 2 0 + 1 2 c$_{m}$P 2 0 ) + c$_{m}$ 2 P$_{0}$M$_{0}$δmδp + 1 2 | ⃗ ∇ δm | 2 + a$_{3}$ 2 | ⃗ ∇ δp | $^{2}$.