Landau Phase Transition

Free Energy

F(φ) = a(T)φ² + bφ⁴ + cφ⁶
a(T) = α(T−Tc)

2nd order: b>0 (c=0)
1st order: b<0 (c>0)

Parameters

Temperature T 0.50 α (T-coefficient) 1.0 b (4th order) 1.0 c (6th order) 0.0 External field h 0.00 Animate T

–

Order parameter φ* –

F(φ*) –

Phase –

About Landau Theory

Landau (1937) expanded free energy in powers of the order parameter φ near the critical temperature Tc. For a 2nd-order transition (b>0), φ changes continuously: φ* ∝ |T−Tc|^β with β=1/2 (mean-field). For a 1st-order transition (b<0, c>0), φ jumps discontinuously. External field h breaks the Z₂ symmetry, preventing exact transition. Real critical exponents differ from mean-field due to fluctuations (Wilson's RG).