Theory and phenomenology for a variety of classical and quantum phase transitions

In this review, we first introduce recent progress in the mathematical structure of the three-dimensional Ising model, from the points of view of topologic, algebraic and geometric aspects. Then we discuss in turn Anderson localization due to disorder and then first- and second-order metal-insulator transitions, depending on electron correlation, with and without a magnetic field. Finally, we make intimate contact with the phase diagram showing the equilibrium between low temperature regimes of the magnetically induced Wigner electron solid and the so-called Laughlin electron liquid in the two-dimensional case.