Landau Theory

Landau Theory is the phenomenological description of a phase transition through an expansion of the free energy in powers of an order parameter, with stable states found where that free energy is at a minimum. The book brings classical phase transition theory into BPT to describe how forms crystallize in the recursive substrate. The order parameter Φ measures how far the field has moved from its critical state; below or above the critical temperature the sign of the quadratic term changes, and the shape of the free energy decides which configurations are stable. A stable form exists where the free energy is stationary and curves upward, ∂F/∂Φ = 0 and ∂²F/∂Φ² > 0. With the order parameter and the diverging correlation length, it makes up the book's framework for critical point behavior. The expansion is F = F_0 + a(T - T_c)Φ² + b*Φ⁴ + ..., where F is the free energy, F_0 a reference free energy, a and b the Landau coefficients of the quadratic and quartic terms, T the system temperature, T_c the critical temperature and Φ the order parameter. Dimensions as this passage's check gives them: F and F_0 [J], a and b [∅], T and T_c [Θ], Φ [𝕃⁻³]; the check is consistent. It connects to Landau Free Energy, Order Parameter, Critical Point Behavior, Critical Exponents and Thresholds of Recursion.