content_image/365046.jpg content_image/365047.jpg content_image/365048.jpg
<img src='content_image/365046.jpg'>

with the correlation lengths: 

<img src='content_image/365047.jpg'>

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. 

<img src='content_image/365048.jpg'>

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. 

