Random quantum Ising spin chains
Random transfer field Ising spin chains are a prototypical example of the interplay between quenched randomness and quantum fluctuations. An approximate real-space renormalization group analysis that becomes exact near the phase zero-temperature phase transition will be presented. Scaling functions and other properties can be computed exactly. Applications of the method to Sinai random walks in random environments, and to higher dimensional random quantum Ising models will be mentioned.