Free energy landscapes, phase transitions, and spontaneous symmetry breaking
Near a phase transition, expand the free energy in powers of the order parameter φ (magnetization, density difference, etc.):
F(φ) = a(T)φ² + bφ⁴ + cφ⁶ − Hφ
With a(T) ∝ (T−T_c): for b>0 gives 2nd order transition, φ* ∝ |t|^(1/2). For b<0 (with c>0) gives 1st order with metastability and a discontinuous jump in φ*.