The free energy as a function ofmis plotted in fig. 139. One can see, that the curvature of the free
energy at the critical temperature is quite small, which leads to large fluctuations during the phase
transition in a real material. (E.g. arising of steam bubbles while heating water to the boiling point)
In our example of the magnetization there would be large areas in the material that are magnetized
while other areas are still unordered atT=TC.
Figure 139: The free energyfas a function of the order parametermfor second order phase transitions
So in our case of ferromagnetism, the magnetization has to exhibit a square root dependence on the
temperature, which coincides very well with experimental datas. (see fig. 140, the circles stand for
experimental datas, the solid line for theoretical predictions)
Figure 140: The magnetization as a function of temperature