GLOBAL PHASE-DIAGRAM IN THE QUANTUM HALL-EFFECT

We report recent progress in determining the global behavior of the two-dimensional electron gas in a high magnetic field. Specifically, we have: (i) derived a law of corresponding states which allows us to construct a global phase diagram and calculate many interrelations between transport coefficients; (ii) derived a "selection rule" governing the allowed continuous transitions between pairs of quantum Hall liquid states; and (iii) identified the "insulating state," which we have named the Hall insulator, as a state in which, as the temperature T --> 0, rho(xx) --> infinity, sigma(xx) and sigma(xy) --> 0, but rho(xy) tends to a constant value, roughly B/nec. Each of these results has many testable experimental consequences.