Applications of classical and quantum theories of critical phenomena to electron and ferroelectric systems

The predictions of the classical theory of critical phenomena are verified by fitting experimental data on the resistivity of the itinerant ferromagnet SrRuO₃ to universal critical functions in order to test published claims in error that this material does not obey universal critical behavior. We find that the data's ‘apparent’ deviations are mainly due to corrections to scaling.; We determine the behavior of the critical temperature of magnetically mediated p-wave superconductivity near a ferromagnetic quantum critical point in three dimensions, distinguishing universal and non-universal aspects of the result. The theory of quantum critical points and the theory of magnetically mediated superconductivity are combined into an eigenvalue problem which is then solved numerically. We find that the transition temperature is non-zero at the critical point, raising the possibility of superconductivity in the ferromagnetic phase.; A realistic theory of the quantum paraelectric-ferroelectric transition is presented, involving parameters determined from band calculations and a renormalization group treatment of critical fluctuations. The effects of reduced dimensionality and deviations from cubic symmetry are determined. Expressions for the pressure dependence of the ferroelectric critical temperature as well as pressure and temperature dependence of the specific heat are derived, and evaluated for realistic materials parameters for the perovskite systems BaTiO ₃ and PbTiO₃. In these materials the ferroelectric soft mode dispersion apparently exhibits a very strong cubic anisotropy, which affects results in an important, albeit quantitative, manner. A change in order parameter orientation from (100) to (111) is predicted as quantum criticality is approached.