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.

Landau was motivated to suggest that the free energy of any system should obey two conditions:

Given these two conditions, one can write down (in the vicinity of the critical temperature, T_c) a phenomenological expression for the free energy as a Taylor expansion in the order parameter.

For example, the Ising model free energy in the vicinity of the phase transition may be written as the following, where the variable ${\displaystyle \Psi }$ is the coarse-grained field of spins, known as the order parameter or the total magnetization.

We can truncate the free energy to the 4th power in ${\displaystyle \Psi }$ without losing the physics of the phase transition, but in general, there are higher order terms present. For the system to be thermodynamically stable, the parameter on the highest even power of the order parameter must be positive. In this case, we find that ${\displaystyle s>0}$, such that the free energy is bound.

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