Past exam of the condensed matter physics major option course of the University of Oxford / 2015 / 3 / b / c / Solution

Along any $⟨111⟩$ direction the quartic term is $(b+c/3)M^4$. Minimizing the amplitude below $T_c$ givesFor the ordered solution,Its free energy is $F_{\min }=F_0-a^2(T_c-T{)}^2/[4(b+c/3)]$. The denominator is positive by the supplied stability assumptions. The square-root onset is the Landau theory exponent; sufficiently close to a three-dimensional critical point, fluctuations can change the actual critical exponent without changing this saddle-point calculation.