Advanced Solid State Physics

For ferroelectricity, one gets the same dependence of the order parameterP on the temperature
(fig. 141) and also the superconductivity exhibits a similar dependence (fig. 142)

Figure 141: The polarization as a function of temperature

Figure 142: The superconductivity as a function of temperature

We now go back to the formula for the free energy and plug in our expression of the order parameter,
to reveal the temperature dependence of the free energy atT < TC:

f=f 0 −

α^20 (T−TC)^2

β

+... (259)

In many applications, the entropySand the specific heatcV are important quantities, so we also want
to compute these atT < TCsince we already know the free energy to test our theory.

s=−

∂f

∂T

=s 0 −

2 α^20 (T−TC)

β

+...

cV=T

∂s

∂T

=c 0 −

2 α^20 T

β

+...