Soft Mode & Structural Phase Transition

A phonon mode softens (ω→0) at the critical wavevector as T→Tc, driving lattice distortion. Below Tc the crystal breaks symmetry and develops a new order parameter.

Soft mode frequency
ω*(T) = 0.00
Order parameter Q
Q = 0.000
Landau theory: F = a(T−Tc)Q² + bQ⁴. Below Tc, Q grows as (Tc−T)^β with β=1/2 (mean field). The soft mode is the fluctuation that condenses: ω²(k*) ∝ (T−Tc).

Examples: perovskite tilts (SrTiO₃), ferroelectric transitions, charge-density waves.