Landau Theory — Symmetry Breaking & Phase Transitions

Landau Free Energy Expansion

F(m) = a(T-Tc)m² + bm⁴ + cm⁶ - hm. The order parameter m (magnetization, density difference, etc.) minimizes F. When b>0: 2nd-order transition at T=Tc — continuous symmetry breaking. When b<0: 1st-order transition with metastable states, hysteresis, and Maxwell construction (equal areas). The phase diagram shows the equilibrium order parameter vs T. The spinodal and binodal lines bound the metastable region. The tricritical point occurs at b=0, c>0.