Advanced Solid State Physics

These results are quite interesting, as one can see that the entropy changes slope at the phase transition
(fig. 143) and the specific heat is linear in temperature but exhibits a discontinuity atTC(fig. 144).
(These figures originally belong to a calculation about superconductivity, but they also hold true
for our computations. The indexnstands for "‘normal"’ andsfor "‘superconducting"’, which is the
material that undergoes the phase transition).

Figure 143: The entropy as a function of temperature

Figure 144: The specific heat as a function of temperature

We now want to take our calculations even further and include a magnetic fieldB, so the formula for
the free energy becomes:

f=f 0 +α 0 (T−TC)m^2 +

1

2

βm^4 −mB (260)

By minimizing the free energy as before, one is left with an expression for small values of the order
parametermatT > TC, which looks similar to the Curie-Weiss law:

m=

B

2 α 0 (T−TC)