Landau Theory

Physics: Landau free energy: F(m) = F₀ + a(T)m² + bm⁴ + cm⁶ − hm; near T_c, a(T) = a₀(T−T_c) changes sign. Second-order transition (b>0): minima at m = ±√(−a/2b) for T0): discontinuous jump in m at the transition; latent heat. Symmetry breaking: for h=0, F(m)=F(−m), but below T_c the system chooses ±m spontaneously. Ginzburg criterion: mean-field theory breaks down when thermal fluctuations dominate, requiring d > d_uc = 4 for the Ising universality class.