Landau theory [SEP] named after
Landau theory
Landau theory in physics is a theory that Lev Landau introduced in an attempt to formulate a general theory of continuous (i.e., second-order) phase transitions.
Mean-field formulation (no long-range correlation).
Landau was motivated to suggest that the free energy of any system should obey two conditions:
- It is analytic.
- It obeys the symmetry of the Hamiltonian.
Given these two conditions, one can write down (in the vicinity of the critical temperature,
Pomeranchuk instability
The Pomeranchuk Instability is an instability in the shape of the Fermi surface of a material with interacting fermions, causing Landau’s Fermi liquid theory to break down. It occurs when a Landau parameter in Fermi liquid theory has a sufficiently negative value, causing deformations of the Fermi surface to be energetically favourable. It is named after the Soviet physicist Isaak Pomeranchuk.
Fermi liquids and Landau parameters.
In a Fermi liquid, renormalized single electron propagators (ignoring spin) are
where capital momentum letters denote four vectors