content_image/362759.jpg content_image/362768.jpg content_image/362769.jpg
## D. Specific heat 

<img src='content_image/362759.jpg'>

In the framework of Ginzburg-Landau theory we may also calculate the specific heat as the second derivative of the free energy. 

<img src='content_image/362768.jpg'>

Providing a similar analysis as in the previous Section we can write down the following expressions for the specific heat valid in the respecting temperature regions: 

<img src='content_image/362769.jpg'>

Where a$_{0}$ = 1 / ( T$_{M}$s$_{h}$m$_{0}$ ), b = 1 / ( s$_{h}$m 3 $_{0}$). The magnetoelectric part Δ C$_{p}$ of the specific heat calculated in this manner is shown in Fig. 9. The mean field values are close to the experimental data below the transition temperature T$_{RM}$ . Essential differences appear above the transition and may be attributed to either short-range or fluctuation effects, as discussed in the next Section. Nevertheless, in spite of the discrepancy in Δ C$_{p}$ the Landau approach predicts the basic characteristics curve of this magnetoelectric system, surprisingly well at low temperatures T < T$_{RM}$ . 

## IV. GAUSSIAN FLUCTUATIONS OF THE ORDER PARAMETERS 

The fluctuations of the magnetization seem to have a small effect on the magnetization curve close to T$_{RM}$ , but there is a discrepancy for the specific heat Δ C$_{p}$ ( T ). Δ C$_{p}$ ( T ) is 

