with two coupled order parameters, as well as compare the results with experiment. This is to show to what extent a simple Landau-type approach can account for the experimental results in a quantitative manner. Our task is related to an even more basic question to what extent ferroelectric order (appearing first at much higher temperature T$_{f}$ ) suppresses the magnetic fluctuations near the corresponding transition temperature T$_{M}$ << T$_{f}$ . In such situation the mean-field description of the magnetic phase should be at least semiquantitatively correct, as we demonstrate below. The structure of the paper is as follows. In Sections II and III we formulate the Landau- theory with two single-component, spatially homogeneous order parameters P and M (rep- resenting the ferroelectric and the ferromagnetic types of order, respectively) coupled via a phenomenological term of the type −| γ | ( PM ) $^{2}$. This coupling leads to a renormalized magnetic transition temperature. In Section III we also compare the results obtained with the data available for BiMnO$_{3}$, as well as introduce a new concept of Arrot plates , which can be used in systems with two coupled order parameters in a ordered state. In Section IV we include Gaussian fluctuations for the coupled system, and subsequently compare the results with experimental data concerning the temperature dependence of the specific heat near the low-temperature magnetic transition. We summarize our results and provide an outlook in Section V. The way to describe the coupling between magnetism and dielectricity in multiferroics was proposed by Smolenskii [17], who explained the origin of the anomaly in the dielectric constant in a ferroelectromagnet within the framework of Landau theory of second-order phase transitions. In the simplest case, the Landau free energy for a system with two coupled order parameters, P and M can be written as: where E$_{a}$ and H$_{a}$ are the applied electric and magnetic fields, respectively. Recently it was shown that this kind of model can discribe the phase transitions on a scale-free network 3 F ( P,M,T ) = F$_{0}$ ( T ) + a$_{0}$ ( T − T$_{M}$ ) 2 M 2 + b 4 M 4 (1) + α$_{0}$ ( T − T$_{f}$ ) 2 P 2 + β 4 P 4 + γ 2 ( PM ) 2 − PE$_{a}$ − MH$_{a}$, II. MEAN FIELD APPROXIMATION: LANDAU APPROACH