LandauGinzburgModelle

The Landau-Ginzburg models are a class of phenomenological theories used to describe second-order phase transitions. Developed by Lev Landau and Vitaly Ginzburg, these models employ an order parameter, a continuous variable that characterizes the state of the system, and an associated free energy functional. The free energy is expressed as a polynomial in the order parameter, with coefficients that depend on temperature.

At temperatures above the critical temperature, the minimum free energy corresponds to a zero value of the order parameter, indicating the disordered phase. As the temperature decreases, the free energy develops a minimum at a non-zero value of the order parameter, signifying the emergence of the ordered phase. The coefficients of the polynomial are chosen such that this transition occurs smoothly at the critical temperature, consistent with the behavior of second-order phase transitions.

The simplest Landau-Ginzburg model involves a scalar order parameter. More complex systems, such as those with vector order parameters or multiple order parameters, can be described by extending the framework. These models have found wide application in various fields, including condensed matter physics (e.g., superconductivity, ferromagnetism, liquid crystals) and statistical mechanics. While phenomenological, they provide valuable qualitative and sometimes quantitative insights into the behavior of systems near phase transitions. The critical exponents derived from Landau-Ginzburg theory often agree with those obtained from more microscopic approaches, especially in dimensions where fluctuations are not dominant.