Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 303 / 1 / b / Solution

At the first-order phase transition, the central minimum $m=0$ and two nonzero minima $m=\pm m_0$ are degenerate, with barriers between them. Writing $x=m_0^2>0$, stationarity and equal free energies giveTheir difference gives $a_{4}x+2a_6{x}^2=0$, soThe magnitude of the magnetization therefore jumps from zero toThe two possible signs are related by the model's spin-reversal symmetry.