Order Parameter & Phase Transition
Lagrangian & Physics
Lagrangian density:
ℒ = ½(∂φ)² − V(φ)
V(φ) = ½μ²φ² + ¼λφ⁴
Minima: φ₀ = ±√(−μ²/λ) if μ²<0
Goldstone boson: massless mode
tangent to vacuum manifold S¹
Domain wall: kink solution
φ(x) = φ₀·tanh(x/ξ), ξ=√(2/|μ²|)
Broken symmetry—
VEV |φ₀|—
Domain walls—
Higgs mass—