Heat-capacity jump in quartic Landau theory (source code)

= Heat-capacity jump in quartic Landau theory
{title2=$\Delta C=T_cb^2/(2d)$}

For zero field, $F=F_0+b(T-T_c)M^2+dM^4$ with $b,d>0$ has ordered minima $M^2=b(T_c-T)/(2d)$ below $T_c$. Minimizing gives $F_{\min}=F_0-b^2(T-T_c)^2/(4d)$. Since $C=-T\partial_T^2F_{\min}$, the ordered-phase excess <heat capacity> is $Tb^2/(2d)$ and its jump relative to the disordered side is $T_cb^2/(2d)$. The value is a total <heat capacity> or a heat-capacity density according to the normalization of $F$.