Thus, below \(T_c\) the system is in the ferromagnetic phase, with one of two possible directions of the average spontaneous magnetization, so that the critical (Curie 39 ) temperature, given by Equat...Thus, below \(T_c\) the system is in the ferromagnetic phase, with one of two possible directions of the average spontaneous magnetization, so that the critical (Curie 39 ) temperature, given by Equation (\ref{72}), marks the transition between the paramagnetic and ferromagnetic phases. (Since the stable minimum value of the free energy \(F\) is a continuous function of temperature at \(T = T_c\), this phase transition is continuous.)
The minimum of the free energy occurs close to the \(h=0\) solution \(m=m\ns_0(\theta)\equiv \sqrt{3}\,(1-\theta)\), and writing \(m=m\ns_0+\delta m\) we find \(\delta m\) to linear order in \(h\) as ...The minimum of the free energy occurs close to the \(h=0\) solution \(m=m\ns_0(\theta)\equiv \sqrt{3}\,(1-\theta)\), and writing \(m=m\ns_0+\delta m\) we find \(\delta m\) to linear order in \(h\) as \(\delta m(\theta,h)=h/2(1-\theta)\).
