Landau Theory

Landau theory is a phenomenological framework for describing continuous phase transitions, developed by Lev Landau in the 1930s. It introduces the concept of an order parameter — a macroscopic variable that is zero in the high-symmetry phase and non-zero in the low-symmetry phase — and constructs the free energy as a power series in this parameter. The key insight is that near the critical point, the details of microscopic interactions become irrelevant; what matters is the symmetry of the order parameter and the dimensionality of the system. Landau theory correctly predicts the qualitative behavior of many phase transitions but fails quantitatively near critical points because it neglects fluctuations. The resolution, developed by Kenneth Wilson through the renormalization group, preserves Landau's symmetry-based approach while incorporating fluctuations to explain universality and critical exponents. Landau's framework remains the conceptual foundation for understanding spontaneous symmetry breaking, superconductivity, and the Higgs mechanism.