FIG. 8: (Color online). Arrot set of planes for the magnetization, calculated for BiMnO$_{3}$ for selected temperatures. The dark plane correspond to the phase transition temperature. The parameters are the same as in the earlier Figures. In the framework of Ginzburg-Landau theory we may also calculate the specific heat as the second derivative of the free energy. 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: 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$_{RM}$ . 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 14 IV. GAUSSIAN FLUCTUATIONS OF THE ORDER PARAMETERS D. Specific heat Δ C$_{p}$ = − T $^{(}$∂ $^{2}$F ∂T 2 ) p . (31) Δ C$_{p}$ =    l ( l − 2 γ$_{m}$ +1) 2( l − γ 2 $_{m}$) · a 2 0 b T for T < T$_{RM}$, l 2 · a 2 0 b T for T > T$_{RM}$.$^{}$   (32)