with the correlation lengths: From Eqs. (59) and (60) we see that when the coherence length is close to zero the correlation function becomes equal to zero as well. On the other hand when the coherence length is large the correlation function decreases as ∝ 1 | ⃗ r$_{2}$ − ⃗ r$_{1}$ $_{|}$, The correlation radii in this region are significantly greater than the lattice constant. We can see that close to ferroelectromagnetic phase transition temperature both coher- ence lengths behave in a similar way. Hence, we assume that below T$_{RM}$ , where both magnetic and electric ordering is observed, the coherence length coalesces as T decreases ( T → 0) (cf. Fig. 11). It can also be seen (from the Fig. 11) that the order parameter cor- responding to the lower critical temperature experience smaller fluctuations near the phase transition. 21 FIG. 11: (Color online). Temperature dependence of the coherence lengths for magnetic (solid line) and electric (dotted line) subsystems calculated for BiMnO$_{3}$. The parameters we use are the same as in the earlier Figures. g$_{m}$ ( ⃗ r$_{1}$, ⃗ r$_{2}$ ) = k$_{B}$T C$_{m}$ · e − √ 2 B$_{m}$ | ⃗ r$_{2}$ − ⃗ r$_{1}$ | 4 π | ⃗ r$_{2}$ − ⃗ r$_{1}$ | ≡ k$_{B}$T C$_{m}$ · e − | ⃗ r 2 − ⃗ r 1 | ξ p 4 π | ⃗ r$_{2}$ − ⃗ r$_{1}$ | , (60) ξ$_{p}$ = √ a$_{3}$ 2 A$_{m}$ , ξ$_{m}$ = √ 1 2 B$_{m}$ . (61)