Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 303 / 1 / a / ii / Solution

At the tricritical point, let ${\alpha }_2=at+O(t^2)$, ${\alpha }_4=bt+O(t^2)$ and ${\alpha }_6(T_c)=u>0$. The nonzero stationarity equation isThe middle term is subleading, so $m^4\sim -at/u$ and $\beta =1/4$. Substitution gives $F_{\min }\asymp -|t{|}^{3/2}$, so the heat capacity behaves as $|t{|}^{-1/2}$ and $\alpha =1/2$.